Search

We present an $SO(10)$ model in which a dimension five operator induces kinetic mixing at the GUT scale between the abelian subgroups $U(1)_{B-L}$ and $U(1)_R$. We discuss in this framework gauge coupling unification and proton decay, as well as the appearance of superheavy quasistable strings with $G\mu \sim 10^{-8} - 10^{-5}$, where $\mu$ denotes the dimensionless string tension parameter. We use Bayesian analysis to show that for $G\mu$ values $\sim 4 \times 10^{-7} - 10^{-5}$, the gravitational wave spectrum emitted from the quasistable strings is in good agreement with the recent pulsar timing array data. Corresponding to $G \mu$ values $\sim 10^{-8} - 2 \times 10^{-7}$, proton decay is expected to occur at a rate accessible in the Hyper-Kamiokande experiment. Finally, we present the gravitational wave spectrum emitted by effectively stable strings with $G\mu\approx 10^{-8}$ that have experienced a certain amount of inflation. This can be tested with future detectors in the $\mu$Hz frequency range., Comment: 18 pages, 5 captioned figures

We present a novel mechanism for producing topologically stable monopoles (TSMs) from the quantum mechanical decay of metastable cosmic strings in the early universe. In an $SO(10)$ model this mechanism yields TSMs that carry two units ($4\pi/e$) of Dirac magnetic charge as well as some color magnetic charge which is screened. For a dimensionless string tension parameter $G\mu \approx 10^{-9} - 10^{-5}$, the monopoles are superheavy with masses of order $10^{15} - 10^{17}$ GeV. Monopoles with masses of order $10^8 - 10^{14}$ GeV arise from metastable strings for $G\mu$ values from $\sim 10^{-22}$ to $10^{-10}$. We identify the parameter space for producing these monopoles at an observable level with detectors such as IceCube and KM3NeT. For lower $G\mu$ values the ultra-relativistic monopoles should be detectable at Pierre Auger and ANITA. The stochastic gravitational wave emission arises from metastable strings with $G\mu\sim 10^{-9}-10^{-5}$ and should be accessible at HLVK and future detectors including the Einstein Telescope and Cosmic Explorer. An $E_6$ extension based on this framework would yield TSMs from the quantum mechanical decay of metastable strings that carry three units ($6\pi/e$) of Dirac magnetic charge., Comment: 21 pages, 6 figures, 1 table

We explore the implications of third family ($t-b-\tau$) quasi-Yukawa unification (QYU) for collider and dark matter (DM) searches within the framework of a supersymmetric $SU(4)_c \times SU(2)_L \times SU(2)_R$ model. The deviation from exact Yukawa unification is quantified through the relation $y_t : y_b : y_\tau = |1+C|:|1-C|:|1+3C|$, with $C$ being a real parameter ($|C| \leq 0.2$). We allow for the breaking of left-right symmetry both by the soft scalar and gaugino mass parameters and obtain a variety of viable solutions that predict the sparticle mass spectrum including LSP DM (whose stability is guaranteed by a $Z_2$ gauge symmetry). We highlight solutions that include an NLSP gluino with mass $\sim$ 1.3-2.5 TeV, which should be accessible at LHC Run 3. There also exist NSLP stop solutions with masses heavier than about 1.8 TeV, which are consistent with the LSP neutralino dark matter relic density through stop-neutralino coannihilation. We identify A-resonance solutions with DM mass $\sim$ 0.8 - 2 TeV, as well as bino-chargino, bino-slepton and bino-stau co-annihilation scenarios. Finally, we also identify Wino-like ($\sim99\%$) and Higgsino-like ($\sim99\%$) solutions whose masses are heavier than about 1.5 TeV and 1 TeV, respectively. These solutions are compatible with the desired dark matter relic density and testable in ongoing and future direct detection experiments., Comment: The revised draft includes Higgsino dark matter solutions and other improvements. Neutralino mixing and RGE evolutions of Yukawa couplings are corrected

Motivated by the NANOGrav 15 year data and other recent investigations of stochastic gravitational background radiation based on pulsar timing arrays, we show how superheavy strings survive inflation but the slightly heavier monopoles do not in a non-supersymmetric hybrid inflation model based on flipped $SU(5)$. With the dimensionless string tension parameter $G \mu\approx 10^{-7}-10^{-6}$, the gravitational wave spectrum emitted by the strings, which are metastable due to breaking caused by monopole-antimonopole quantum mechanical tunneling, is compatible with the latest NANOGrav measurement as well as the advanced LIGO-VIRGO third run data. For $G \mu \approx 10^{-6}$, the string network undergoes about 30 $e$-foldings of inflation which suppresses the spectrum in the LIGO-VIRGO frequency range. With the symmetry breaking chain $SU(5) \times U(1)_X \to SU(3)_c \times SU(2)_L\times U(1)_Z \times U(1)_X \to SU(3)_c \times SU(2)_L \times U(1)_ Y$, the estimated proton lifetime is of order $10^{34}-10^{36}$ yrs., Comment: 18 pages, 2 figures and 5 tables. Additional references and two footnotes have been included in version 2

The latest FermiLab muon $g-2$ result shows a $5\sigma$ discrepancy with a ``widely advertised" Standard Model prediction. We consider a supersymmetric $SU(4)_c \times SU(2)_L \times SU(2)_R$ model in which this discrepancy is resolved by including contributions to muon $g-2$ from a relatively light SUSY sector. A variety of realistic coannihilation scenarios can reproduce the observed dark matter relic abundance. With a significantly reduced discrepancy, of order $1 \sigma$ or less, the Higgsino-like dark matter solutions are also viable. We provide benchmark points for these solutions that will be probed in the direct detection dark matter experiments and collider searches.

Renormalisation group analysis with the present measurements of the top quark mass $m_t = 172.69\pm 0.30$ GeV indicates that the Standard Model (SM) Higgs potential becomes unstable at energy scales $\sim 10^{10}$ GeV. This may be interpreted as hinting at new particles at high energy. The minimal extension of the SM that can avoid this instability while leaving the SM Higgs as the sole scalar particle of the theory is obtained by adding suitable fermions to the SM. These fermions are good dark matter candidates and the model is known as the minimal dark matter model. We revisit the inflationary scenario based on the minimal dark matter model, taking into account updated parameter constraints and recent understanding of reheating dynamics. We explore the model with different values of the right-handed neutrino mass and find that the cosmological prediction is insensitive to such details. We obtained a spectral index of the cosmic microwave background $n_s=0.9672$ and a tensor-to-scalar ratio $r=0.0031$ as a robust prediction of this scenario., Comment: 8 pages, 2 figures; v2: references added

Composite topological structures such as ``superheavy quasi-stable strings" and ``walls bounded by strings" arise in realistic extensions of the Standard Model of high energy physics. We show that the gravitational radiation emitted in the early universe by these two unstable structures, with a dimensionless string tension $G\mu\approx 10^{-6}$, is consistent with the NANOGrav discovery of low frequency gravitational background, as well as the recent LIGO-VIRGO constraints, provided the superheavy strings and monopoles experience a certain amount of inflation. For the case of walls bounded by strings, the domain wall arises from the spontaneous breaking of a remnant discrete gauge symmetry around the electroweak scale. The quasi-stable strings, on the other hand, arise from a two step breaking of a local gauge symmetry. The monopoles appear from the first breaking and get connected to strings that arise from the second breaking. Both composite structures decay by emitting gravitational waves over a wide frequency range., Comment: 8 pages, 4 captioned figures

We investigate the inflationary cosmology involving an SU(5) GUT (grand unified theory) singlet scalar with non-minimal coupling to the Ricci scalar. In this scenario the scale of grand unification is set by the inflaton vev when the inflaton rolls down its potential towards its minimum $v$, thereby relating inflationary dynamics to GUT symmetry breaking with a prediction $r \simeq 0.025$ for the tensor-to-scalar ratio to be tested by the next generation CMB experiments. We show in this inflationary framework involving inflection-point how a suitable choice of parameters in $SU(5)$ leads to a bump in the scalar power spectrum with production of Primordial Blackholes (PBH) of masses $10^{17}-10^{18}$g ($ 10 - 100 M_\odot$). We derive the constraints on the self quartic and mixed quartic couplings of the inflaton in SU(5) that are consistent with the inflationary analysis. Moreover, we also show that this scenario leads to large amplitude induced second-order tensor perturbations propagating as Gravitational Waves (GW) with amplitude $\Omega_{\rm GW}h^2 \sim 10^{-17}$ and peak frequency $f_{\rm peak} \sim$ (0.1 - 1) Hz, which can be detected in the next generation GW observatories like LISA, BBO, ET, etc. Thus, we unify the $SU(5)$ framework with PBH via inflection-point inflation showing how the upcoming measurements of PBH and GW will enable us to probe the scale of $SU(5)$ symmetry breaking, and thereby complementing the laboratory based experiments. We also discuss scenarios involving the Pati-Salam and Trinification gauge groups and its impact on quartic and mixed-quartic couplings that may lead to PBH and detectable GW signals., Comment: In the revised version any inadvertent text overlap with other papers has been removed, the appendix is removed, and previous sections 5 and 6 have been merged. All results including figures and conclusions remain intact

We explore the gravitational wave spectrum generated by string-wall structures in an $SO(10)$ ($Spin(10)$) based scenario of pseudo-Goldstone boson dark matter (pGDM) particle. This dark matter candidate is a linear combination of the Standard Model (SM) singlets present in the 126 and 16 dimensional Higgs fields. The Higgs $126$-plet vacuum expectation value (VEV) $\left<126_H\right>$ leaves unbroken the $\mathbb{Z}_2$ subgroup of $\mathbb{Z}_4$, the center of $SO(10)$. Among other things, this yields topologically stable cosmic strings with a string tension $\mu \sim \left<126_H\right>^2$. The subsequent (spontaneous) breaking of $\mathbb{Z}_2$ at a significantly lower scale by the $16$-plet VEV $\left<16_H\right>$ leads to the appearance of domain walls bounded by the strings produced earlier. We display the gravitational wave spectrum for $G \mu$ values varying between $10^{-15}$ and $10^{-9}$ ($\left<126_H\right>\sim 10^{11}$ - $10^{14}$ GeV), and $\left<16_H\right>\sim 0.1$ - $10^2$ TeV range ($G$ denotes Newton's constant.) These predictions can be tested, as we show, by a variety of (proposed) experiments including LISA, ET, CE and others., Comment: 8 pages, 3 figures, version published in PLB

We explore a variety of composite topological structures that arise from the spontaneous breaking of $SO(10)$ to $SU(3)_c \times U(1)_{em}$ via one of its maximal subgroups $SU(5) \times U(1)_\chi$, $SU(4)_c \times SU(2)_L \times SU(2)_R$, and $SU(5) \times U(1)_X$ (also known as flipped $SU(5)$). They include i) a network of $\mathbb{Z}$ strings which develop monopoles and turn into necklaces with the structure of $\mathbb{Z}_2$ strings, ii) dumbbells connecting two different types of monopoles, or monopoles and antimonpoles, iii) starfish-like configurations, iv) polypole configurations, and v) walls bounded by a necklace. We display these structures both before and after the electroweak breaking. The appearance of these composite structures in the early universe and their astrophysical implications including gravitational wave emission would depend on the symmetry breaking patterns and scales, and the nature of the associated phase transitions.

We estimate the stochastic gravitational wave spectrum emitted from a network of cosmic strings in which the latter are effectively stable against breaking by monopole pair creation. The monopoles are produced at a higher scale from an earlier symmetry breaking and experience significant inflation before reentering the horizon. This gives rise to monopole-antimonopole pairs connected by string segments and the string loop formation essentially ceases. As a consequence, the lower frequency portion of the gravitational wave spectrum is suppressed relative to the no-inflation case with stable strings, which evades the stringent PPTA bound on the dimensionless string tension $G\mu$. We display the modified spectrum, accessible in the ongoing and future experiments, for $G\mu$ values in the range $10^{-10} - 10^{-15}$. We show how this `quasi-stable' string network is realized in realistic grand unified theories., Comment: 18 pages, 7 figures

We present a successful realization of supersymmetric $\mu$-hybrid inflation model based on a gauged $U(1)_{B-L}$ extension of the minimal supersymmetric standard model, with the soft supersymmetry breaking terms are playing an important role. Successful non-thermal leptogenesis with gravitino dark matter yields a reheat temperature in the range $2 \times 10^{7} \lesssim T_R \lesssim 5 \times 10^{9}$ GeV. This corresponds to the predictions $2 \times 10^{-18} \lesssim r\lesssim 4 \times 10^{-13}$ for the tensor to scalar ratio, and $-2 \times 10^{-6} \lesssim dn_s/d\ln k \lesssim -5 \times 10^{-11}$ for the running of the scalar spectral index. The $B-L$ breaking scale is estimated as $ 6 \times 10^{14}\lesssim M/ \text{GeV}\lesssim 10^{16}$, calculated at the central value of the scalar spectral index, $n_s =0.9655$, reported by Planck 2018. Finally, in a grand unified theory setup the dimensionless string tension parameter associated with the metastable strings is in the range $ 10^{-9} \lesssim G\mu_\text{cs} \lesssim 10^{-6}$ corresponding to a stochastic gravitational wave background lying within the 2$\sigma$ bound of the recent NANOGrav 12.5-yr data., Comment: 12 pages, 7 figures

Inspired by the recent determination of the $W$-boson mass by the CDF collaboration, we revisit an SO(10) axion model in which a scalar $SU(2)_L$ triplet field with zero hypercharge is known to acquire a non-zero VEV through its mixing with the Standard Model Higgs doublet. The triplet VEV provides a sizable contribution to the W mass, which helps in significantly lowering the $7\sigma$ discrepancy between the SM prediction and the higher CDF value for $m_W$. We show that the relatively light triplet mass ($\sim (1-50)$ TeV) is compatible with gauge coupling unification and observable proton decay. An unbroken $Z_2$ gauge symmetry, coupled with the presence of two fermionic $10$-plets required to resolve the axion domain wall problem, means that both axions and a stable intermediate mass ($\sim 10^9-10^{10}$ GeV) fermion are plausible dark matter candidates. We also display the gravitational wave spectrum from the intermediate scale topologically stable cosmic strings predicted by the model., Comment: 18 pages, 6 figures

Motivated by the recently reported measurement of the $W$ boson mass $M_W = 80.4335 \pm 0.0094$ GeV by the CDF collaboration, we propose a type III extension of the minimal supersymmetric standard model (MSSM) which also includes an R-parity violating term. Without taking potential SUSY radiative corrections into account, we show that the CDF measurement of $M_W$ and the LEP measurement of the $\rho$ parameter can be simultaneously accommodated at the $2 \sigma$ level. A long-lived gravitino in a few GeV mass range is a unique viable dark matter candidate in this framework., Comment: 3 pages, typos corrected and references added

The International Linear Collider (ILC) is on the table now as a new global energy-frontier accelerator laboratory taking data in the 2030s. The ILC addresses key questions for our current understanding of particle physics. It is based on a proven accelerator technology. Its experiments will challenge the Standard Model of particle physics and will provide a new window to look beyond it. This document brings the story of the ILC up to date, emphasizing its strong physics motivation, its readiness for construction, and the opportunity it presents to the US and the global particle physics community., Comment: 356 pages, Large pdf file (40 MB) submitted to Snowmass 2021; v2 references to Snowmass contributions added, additional authors

We explore the implications of resolving the muon g-2 anomaly in a SU(4)_c x SU(2)_L x SU(2)_R model, where the soft supersymmetry breaking scalar and gaugino masses break the left-right (LR) symmetry. A 2 sigma resolution of the anomaly requires relatively light sleptons, chargino and LSP neutralino. The stau turns out to be the NLSP of mass <~ 400 GeV, and the sleptons from the first two families can be as heavy as about 800 GeV. The chargino is also required to be lighter than about 600 GeV to accommodate the muon g-2 solutions consistent with the dark matter relic density constraint. The dominant right-handed nature of the light slepton states suppress the sensitivity of possible signals which can be probed in Run3 experiments at the LHC. We also discuss the impact of accomodating the Higgs boson mass and the vacuum stability of the scalar potential for these solutions. The Higgsinos are heavier than about 4 TeV, and the LSP neutralino has the correct relic density if it is Bino-like. We identify stau-neutralino coannihilation as the dominant mechanism for realizing the desired dark matter relic density, with sneutrino-neutralino coannihiliation playing a minor role. These bino-like dark matter solutions can yield a spin-independent scattering cross-section on the order of 10^{-3} pb which hopefully, can be expected to be tested in the near future.

We study the low energy implications of a trinification model based on the gauge symmetry $G= SU(3)_c \times SU(3)_L \times SU(3)_R$, without imposing gauge coupling unification. A minimal model requires two Higgs multiplets that reside in the bi-fundamental representation of $G$, and this is shown to be adequate for accommodating the Standard Model (SM) fermion masses and generate, via loop corrections and seesaw mechanism, suitable masses for the heavy neutral leptons as well as the observed SM neutrinos. We estimate a lower bound of around 15 TeV for the masses of the new down-type quarks that are required by the $SU(3)_L \times SU(3)_R$ symmetry. We examine the resonant production at the LHC of the new gauge bosons, which leads to a lower bound of 16 TeV for the symmetry breaking scale of $G$. We also show how the muon $g-2$ anomaly can be resolved in the presence of these new gauge bosons and the heavy charged leptons present in the model. Finally, the model predicts the presence of a topologically stable monopole carrying three quanta $(6 \pi /e)$ of Dirac magnetic charge and mass $\gtrsim 160$ TeV. If new matter fields lying in the fundamental representations of G are included, the model predicts the presence of exotic leptons, mesons and baryons carrying fractional electric charges such as $\pm e/3$ and $\pm 2e/3$, fully compatible with the Dirac quantization condition., Comment: 27 pages and references, 5 figures

We discuss some testable predictions of a non-supersymmetric $SO(10)$ model supplemented by a Peccei-Quinn symmetry. We utilize a symmetry breaking pattern of $SO(10)$ that yields unification of the Standard Model gauge couplings, with the unification scale also linked to inflation driven by an $SO(10)$ singlet scalar field with a Coleman-Weinberg potential. Proton decay mediated by the superheavy gauge bosons may be observable at the proposed Hyper-Kamiokande experiment. Due to an unbroken $Z_2$ gauge symmetry from $SO(10)$, the model predicts the presence of a stable intermediate mass fermion which, together with the axion, provides the desired relic abundance of dark matter. The model also predicts the presence of intermediate scale topologically stable monopoles and strings that survive inflation. The monopoles may be present in the Universe at an observable level. We estimate the stochastic gravitational wave background emitted by the strings and show that it should be testable in a number of planned and proposed space and land based experiments. Finally, we show how the observed baryon asymmetry in the Universe is realized via non-thermal leptogenesis., Comment: 36 pages, 9 figures, version published in JCAP

We discuss how in $SO(10)$ grand unification an observable number density of topologically stable intermediate mass ( $\sim 10^{14}$ GeV) monopoles survive inflation driven by a Coleman-Weinberg potential and non-minimal coupling of the inflaton field to gravity. The scalar spectral index $n_s$ is in excellent agreement with the current observations, and the tensor to scalar ratio $r\gtrsim 0.003$. The model also predicts the presence of intermediate scale topologically stable cosmic strings, and their gravitational wave spectrum reflects the amount of cosmic inflation experienced by the associated symmetry breaking. The discovery of these primordial monopoles and the stochastic gravitational wave background from the strings would provide important new insights regarding the symmetry breaking patterns in the early universe., Comment: 21 pages, 10 figures, matches version published in JCAP

We explore some experimentally testable predictions of an $SO(10)$ axion model which includes two 10-plets of fermions in order to resolve the axion domain wall problem. The axion symmetry can be safely broken after inflation, so that the isocurvature perturbations associated with the axion field are negligibly small. An unbroken gauge $Z_2$ symmetry in $SO(10)$ ensures the presence of a stable WIMP-like dark matter, a linear combination of the electroweak doublets in the fermion 10-plets and an $SO(10)$ singlet fermion with mass $\sim 62.5 \; {\rm GeV}\; (1 \; {\rm TeV}) $ when it is mostly the singlet (doublet) fermion, that co-exists with axion dark matter. We also discuss gauge coupling unification, proton decay, inflation with non-minimal coupling to gravity and leptogenesis. With the identification of the SM singlet Higgs field in the $126$ representation of $SO(10)$ as inflaton, the magnetic monopoles are inflated away, and we find $0.963 \lesssim n_s \lesssim 0.965$ and $0.003 \lesssim r \lesssim 0.036$, where $n_s$ and $r$ denote the scalar spectral index and tensor-to-scalar ratio, respectively. These predictions can be tested in future experiments such as CMB-S4., Comment: 21 pages, 6 figures

Inspired by the recent determination of the $W$-boson mass by the CDF collaboration, we revisit an $SO(10)$ axion model in which a scalar $SU(2)_L$ triplet field with zero hypercharge is known to acquire a non-zero VEV through its mixing with the Standard Model Higgs doublet. The triplet VEV provides a sizable contribution to the $W$ mass, which helps in significantly lowering the $7\sigma$ discrepancy between the Standard Model prediction and the higher CDF value for $m_W$. We show that the relatively light triplet mass ($\sim (1-50)$ TeV) is compatible with gauge coupling unification and observable proton decay. An unbroken $Z_2$ gauge symmetry, coupled with the presence of two fermionic $10$-plets required to resolve the axion domain wall problem, means that both axions and a stable intermediate mass ($\sim 10^9-10^{10}$ GeV) fermion are plausible dark matter candidates. We also display the gravitational wave spectrum from the intermediate scale topologically stable cosmic strings predicted by the model., Comment: 20 pages, 6 figures, published version

We show how in the standard electroweak model three $SU(2)_L$ Nambu monopoles, each carrying electromagnetic (EM) and Z- magnetic fluxes, can merge (through Z-strings) with a single $U(1)_Y$ Dirac monopole to yield a composite monopole that only carries EM magnetic flux. Compatibility with the Dirac quantization condition requires this composite monopole to carry six quanta ($12 \pi /e$) of magnetic charge, independent of the electroweak mixing angle $\theta_w$. The Dirac monopole is not regular at the origin and the energy of the composite monopole is therefore divergent. We discuss how this problem is cured by embedding $U(1)_Y$ in a grand unified group such as $SU(5)$. A second composite configuration with only one Nambu monopole and a colored $U(1)_Y$ Dirac monopole that has minimal EM charge of $4\pi/e$ is also described. Finally, there exists a configuration with an EM charge of $8\pi/e$ as well as screened color magnetic charge., Comment: 4 pages, 2 figures; published (PRD) version

We propose a pseudo-Goldstone boson dark matter (pGDM) particle in $SO(10)$ grand unified theory (GUT). Due to its Goldstone nature, this pGDM evades the direct DM detection experiments which, otherwise, severely constrain the parameter space of DM models. In $SO(10)$, the pGDM is embedded as a linear combination of the Standard Model (SM) singlet scalars in ${\bf 16_H}$ and ${\bf 126_H}$ representations. We consider two scenarios for the intermediate route of $SO(10)$ symmetry breaking (SB) to the SM: $SU(5) \times U(1)_X$ and Pati-Salam the $SU(4)_c \times SU(2)_L \times SU(2)_R$ (4-2-2) gauge groups. The vacuum expectation value of ${\bf 126_H}$, which triggers the breaking of $U(1)_X$ and 4-2-2 symmetry in the two scenarios, respectively, determines the pGDM lifetime whose astrophysical lower bound provides one of the most stringent constraints. For the 4-2-2 route to $SO(10)$, the successful SM gauge coupling unification requires the 4-2-2 breaking scale to be ${\cal O} (10^{11})$ GeV, and most of the parameter space is excluded. For the $SU(5) \times U(1)_X$ route, on the other hand, the $U(1)_X$ breaking scale can be significantly higher, and a wide range of the parameter space is allowed. Furthermore, the proton lifetime in the $SU(5)$ case is predicted to be $4.53 \times 10^{34}$ years, which lies well within the sensitivity reach of the Hyper-Kamiokande experiment. We also examine the constraints on the model parameter space from the Large Hadron Collider and the indirect DM search by Fermi-LAT and MAGIC experiments., Comment: 25 pages, 5 figures, Figures 3 revised, updated version accepted for publication in PRD

We consider a $U(1)_{B-L}$ model with a $Z^\prime$ portal Dirac fermion dark matter (DM) $\chi$ of low mass which couples very weakly to the $B - L$ gauge boson $Z^\prime$. An arbitrary $B-L$ charge $Q\neq \pm1, \pm 3$ of the DM $\chi$ ensures its stability. Motivated by the sensitivity reach of forthcoming "Lifetime Frontier" experiments, we focus on the $Z^\prime$ mass, $m_{Z^\prime}$, in the sub-GeV to few GeV range. To evaluate the DM relic abundance, we examine both the freeze-out and freeze-in DM scenarios. For the freeze-out scenario, we show that the observed DM abundance is reproduced near the $Z^\prime$ resonance, $m_\chi \simeq m_{Z^\prime}/2$, where $m_\chi$ is the DM mass. For the freeze-in scenario, we focus on $m_\chi \ll m_{Z^\prime}$. We show that for a fixed value of $m_{Z^\prime}$, $g_{BL}$ values roughly scale as $1/Q$ to reproduce the observed DM abundance. For various $Q$ values in the range between $10^{-6}$ and $10^2$, we show that the gauge coupling values $g_{BL}$ needed to reproduce the observed DM abundance lie in the search reach of future planned and/or proposed experiments such as FASER, Belle-II, LDMX, and SHiP. In the freeze-in case, the $Q$ values to realize observable $g_{BL}$ values are found to be much smaller than that in the freeze-out case., Comment: 13 pages, 2 figures

We present a successful realization of sneutrino tribrid inflation model based on a gauged $U(1)_{B-L}$ extension of Minimal Supersymmetric Standard Model (MSSM). A single interaction term involving the $B-L$ Higgs field and the right-handed neutrinos serves multiple purposes. These include the generation of heavy Majorana masses for the right-handed neutrinos to provide an explanation for the tiny neutrino masses via the seesaw mechanism, a realistic scenario for reheating and non-thermal leptogenesis with a reheat temperature as low as $10^6$ GeV, and a successful realization of inflation with right-handed sneutrino as the inflaton. The matter parity which helps avoid rapid proton decay survives as a $Z_{2}$ subgroup of a $U(1)$ $R$-symmetry. Depending on the choice of model parameters yields the following predicted range of the tensor to scalar ratio, $3 \times 10^{-11}\lesssim r\lesssim 7\times 10^{-4}$ ($ 6 \times 10^{-7} \lesssim r \lesssim 0.01 $), and the running of the scalar spectral index, $-0.00022 \lesssim dn_s/d\ln k \lesssim -0.0026$ ($-0.00014 \lesssim dn_s/d\ln k \lesssim 0.005$), along with the $B-L$ breaking scale, $ 3 \times 10^{14}\lesssim M/ \text{GeV}\lesssim 5 \times 10^{15}$ ($ 6 \times 10^{15}\lesssim M/ \text{GeV}\lesssim 2 \times 10^{16}$), calculated at the central value of the scalar spectral index, $n_s =0.966$, reported by Planck 2018. The possibility of realizing metastable cosmic strings in a grand unified theory setup is briefly discussed. The metastable cosmic string network admits string tension values in the range $10^{-8} \lesssim G\mu_s \lesssim 10^{-6}$, and predicts a stochastic gravitational wave background lying within the 2-$\sigma$ bounds of the recent NANOGrav 12.5-yr data., Comment: 32 pages, 9 figures; JCAP published version

Inspired by the latest measurement of muon g-2 by the Fermilab Experiment, we revisit a class of supersymmetric models in which non-universality at M_GUT allows us to realize relatively light sleptons in the few hundred GeV range. These sleptons provide additional contributions to muon g-2 that can be arranged to reconcile theory and experiment. The solutions compatible with the muon g-2 resolution typically predict light sleptons, charginos and neutralinos. We show how these solutions can be probed during LHC-Run3. A direct impact on the chargino mass is observed such that the chargino can be probed up to about 800 GeV during the Run3 experiments. Despite such a direct impact, it is still possible to realize lighter chargino masses which can escape detection due to the chirality mixture of the lighter slepton states. The colored squarks as well as the gluino turn out to be heavier than about 3-4 TeV if the LSP neutralino satisfies the Planck bound on the dark matter relic abundance. We highlight a variety of benchmark points and, in particular, coannihilation scenarios with dark matter candidates that will be tested in the ongoing and planned direct and indirect detection experiments. By relaxing the requirement that the LSP neutralino saturates the relic dark matter abundance, we are able to find solutions with gluino and squark masses in a range that may be accessible at LHC-Run3.

We have realized non-minimal Higgs inflation and standard hybrid inflation in the supersymmetric flipped $SU(5)$ model with $U(1)_R$ symmetry using the no-scale form of the K\"{a}hler potential. In non-minimal Higgs inflation the waterfall Higgs field plays the role of inflaton, and in standard hybrid inflation the gauge singlet field $S$ is employed as an inflaton. The predictions of both models are in good agreement with the Planck 2018 data. For numerical calculations we have fixed the gauge symmetry breaking scale, $M$, around $2\times 10^{16}$ GeV. In both models the inflaton field values are constrained below $m_P$. The tensor to scalar ratio $r$ in non-minimal inflation is of the order of $10^{-3}$ and for standard hybrid inflation $r$ is tiny, of order $10^{-15} - 10^{-4}$. The scalar spectral index in both cases lie within the Planck 1-$\sigma$ bounds, and the running of the scalar spectral index lies in the range, $-dn_s/d\ln k \sim 6\times 10^{-4}$ for non-minimal model and $10^{-9} - 10^{-3}$ for the standard hybrid model. A realistic scenario of reheating and non-thermal leptogenesis is employed with reheat temperature $T_r \sim 10^9$ GeV for non-minimal model and $10^{6} - 10^{10}$~GeV for standard hybrid model. The $R$-symmetry plays a vital role in forbidding rapid proton decay, but at the same time it also suppresses terms responsible for generating right handed neutrino masses. A realistic scenario of right handed neutrino masses is obtained by considering effective $R$ symmetry breaking at the nonrenormalizable level with adequate suppression of rapid proton decay., Comment: 26 pages, 10 figures, matches with the published version

We propose a $SU(5) \times U(1)_X \times U(1)_{PQ}$ model, where $U(1)_X$ is the generalization of the $B-L$ (baryon minus lepton number) gauge symmetry and $U(1)_{PQ}$ is the global Peccei-Quinn (PQ) symmetry. There are four fermions families in $\bf{{\overline 5}} + \bf{10}$ representations of $SU(5)$, a mirror family in $\bf{5}+\bf{{\overline {10}}}$ representations, and three $SU(5)$ singlet Majorana fermions. The $U(1)_X$ related anomalies all cancel in the presence of the Majorana neutrinos. The $SU(5)$ symmetry is broken at $M_{GUT} \simeq (6-9)\times 10^{15}$ GeV and the proton lifetime $\tau_p$ is estimated to be well within the expected sensitivity of the future Hyper-Kamiokande experiment, $\tau_p \lesssim 1.3 \times 10^{35}$ years. The $SU(5)$ breaking also triggers the breaking of the PQ symmetry, resulting in axion dark matter (DM), with the axion decay constant $f_a$ of order $M_{GUT}$ or somewhat larger. The CASPEr experiment can search for such an axion DM candidate. The Hubble parameter during inflation must be low, $H_{inf} \lesssim 10^9 $ GeV, in order to successfully resolve the axion domain wall, axion DM isocurvature and $SU(5)$ monopole problems. With the identification of the $U(1)_X$ breaking Higgs field with the inflaton field, we implement inflection-point inflation, which is capable of realizing the desired value for $H_{inf}$. The vectorlike fermions in the model are essential for achieving successful unification of the SM gauge couplings as well as the phenomenological viability of both axion DM and inflation scenario., Comment: 20 pages, 3 figures, Figures 1 and 2 revised, updated version accepted for publication in PRD

We use the $SU(5)$ model to show the presence in grand unified theories of an electroweak monopole and a magnetic dumbbell ("meson") made up of a monopole-antimonopole pair connected by a $Z$-magnetic flux tube. The monopole is associated with the spontaneous breaking of the weak $SU(2)_L$ gauge symmetry by the induced vacuum expectation value of a heavy scalar $SU(2)_L$ triplet with zero weak hypercharge contained in the adjoint Higgs 24-plet. This monopole carries a Coulomb magnetic charge of $(3/4) (2\pi/e)$ as well as $Z$-magnetic charge, where $2\pi/e$ denotes the unit Dirac magnetic charge. Its total magnetic charge is $\sqrt{3/8}(4\pi/e)$, which is in agreement with the Dirac quantization condition. The monopole weighs about 700 GeV, but because of the attached $Z$-magnetic tube it exists, together with the antimonopole, in a magnetic dumbbell configuration whose mass is expected to lie in the TeV range. The presence of these topological structures in $SU(5)$ and $SO(10)$ and in their supersymmetric extensions provides an exciting new avenue for testing these theories in high-energy colliders., Comment: 5 pages, version published in Phys. Rev. D

We investigate the impact of Coleman-Weinberg inflation on the stochastic gravity wave background spectrum emitted by intermediate scale cosmic strings. The string network is partially inflated and re-enters the horizon at later times after the end of inflation, such that the short string loops are not produced. This leads to a significant modification of the gravity wave spectrum that we explore in detail. We find that Coleman-Weinberg inflation can help to satisfy the Parkes Pulsar Timing Array (PPTA) bound for dimensionless string tension values in the range $G\mu > 1.1\times 10^{-10}$. We also identify the modified gravity wave spectra which, in the case of inflation, are compatible with the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) data. We then discuss the formation of monopoles and strings at the same breaking scale and the compatibility of the Monopole, Astrophysics and Cosmic Ray Observatory (MACRO) bound with the PPTA bound, and also with the NANOGrav data. Finally, an example of a realistic non-supersymmetric $E_6$ model incorporating successful Coleman-Weinberg inflation is presented in which monopoles and strings both survive inflation and are present at an observable level., Comment: 8 pages, Two columns, 12 figures, Version to appear in PRD

We describe the internal composition of a topologically stable monopole carrying a magnetic charge of $6\pi/e$ that arises from the spontaneous breaking of the trinification symmetry $SU(3)_c\times SU(3)_L\times SU(3)_R$ ($G$). Since this monopole carries no color magnetic charge, a charge of $6\pi/e$ is required by the Dirac quantization condition. The breaking of $G$ to the Standard Model occurs in a number of steps and yields the desired topologically stable monopole ("magnetic baryon"), consisting of three confined monopoles. The confined monopoles ("magnetic quarks") each carry a combination of Coulomb magnetic flux and magnetic flux tubes, and therefore they do not exist as isolated states. We also display a more elaborate configuration ("fang necklace") composed of these magnetic quarks. In contrast to the $SU(5)$ monopole which is superheavy and carries a magnetic charge of $2\pi/e$ as well as color magnetic charge, the trinification monopole may have mass in the TeV range, in which case it may be accessible at the LHC and its planned upgrades., Comment: 11 pages including 2 figures, version published in Phys. Lett. B

A gauged $U(1)_X$ symmetry appended to the Standard Model (SM) is particularly well-motivated since it can account for the light neutrino masses by the seesaw mechanism, explain the origin of baryon asymmetry of the universe via leptogenesis, and help implement successful cosmological inflation with the $U(1)_X$ breaking Higgs field as the inflaton. In this framework, we propose a light dark matter (DM) scenario in which the $U(1)_X$ gauge boson $Z^\prime$ behaves as a DM particle in the universe. We discuss how this scenario with $Z^\prime$ mass of a few keV and a $U(1)_X$ gauge coupling $g_X \simeq 10^{-16}$ can nicely fit the excess in the electronic recoil energy spectrum recently reported by the XENON1T collaboration. In order to reproduce the observed DM relic density in the presence of such a tiny gauge coupling, we propose an extension of the model to a two-component DM scenario. The $Z^\prime$ DM density can be comparable to the observed DM density by the freeze-in mechanism through the coupling of $Z^\prime$ boson to a partner Higgs-portal scalar DM with a large $U(1)_X$ charge., Comment: 6 pages, version published in PLB

We investigate supersymmetric hybrid inflation in a realistic model based on the gauge symmetry $SU(4)_c \times SU(2)_L \times SU(2)_R$. The minimal supersymmetric standard model (MSSM) $\mu$ term arises, following Dvali, Lazarides, and Shafi, from the coupling of the MSSM electroweak doublets to a gauge singlet superfield which plays an essential role in inflation. The primordial monopoles are inflated away by arranging that the $SU(4)_c \times SU(2)_L \times SU(2)_R$ symmetry is broken along the inflationary trajectory. The interplay between the (above) $\mu$ coupling, the gravitino mass, and the reheating following inflation is discussed in detail. We explore regions of the parameter space that yield gravitino dark matter and observable gravity waves with the tensor-to-scalar ratio $r \sim 10^{-4}-10^{-3}$., Comment: 14 pages, 9 figures; version published in Phys. Rev. D

We consider a U(1)$_X$ gauge symmetry extension of the Standard Model (SM) with a $Z^\prime$-portal Majorana fermion dark matter that allows for a relatively light gauge boson $Z^\prime$ with mass of 10 MeV$-$ a few GeV and a much heavier dark matter through the freeze-in mechanism. In a second scenario the roles are reversed, and the dark matter mass, in the keV range or so, lies well below the $Z^\prime$ mass, say, $\sim 1$ GeV. We outline the parameter space that can be explored for these two scenarios at the future Lifetime Frontier experiments including Belle-II, FASER, LDMX and SHiP., Comment: 18 pages, 4 figures, new references added, typos corrected

We investigate a non-supersymmetric $SO(10)\times U(1)_{\rm PQ}$ axion model in which the spontaneous breaking of $U(1)_{\rm PQ}$ occurs after inflation, and the axion domain wall problem is resolved by employing the Lazarides-Shafi mechanism. This requires the introduction of two fermion 10-plets, such that the surviving discrete symmetry from the explicit $U(1)_{\rm PQ}$ breaking by QCD instantons is reduced from $Z_{12}$ to $Z_4$, where $Z_4$ coincides with the center of $SO(10)$ (more precisely $Spin(10)$). An unbroken $Z_2$ subgroup of $Z_4$ yields intermediate scale topologically stable strings, as well as a stable electroweak doublet non-thermal dark matter candidate from the fermion 10-plets with mass comparable to or somewhat smaller than the axion decay constant $f_{\rm a}$. We present an explicit realization with inflation taken into account and which also incorporates non-thermal leptogenesis. The fermion dark matter mass lies in the $3\times 10^{8}-10^{10}~{\rm GeV}$ range and its contribution to the relic dark matter abundance can be comparable to that from the axion., Comment: 9 pages, 5 figures included, version to be published in Phys. Lett. B

Gauging the global $B-L$ (Baryon number minus Lepton number) symmetry in the Standard Model (SM) is well-motivated since anomaly cancellations require the introduction of three right-handed neutrinos (RHNs) which play an essential role in naturally generating tiny SM neutrino masses through the seesaw mechanism. In the context of the $B-L$ extended SM, we propose a pseudo-Goldstone boson dark matter (DM) scenario in which the imaginary component of a complex $B-L$ Higgs field serves as the DM in the universe. The DM relic density is determined by the SM Higgs boson mediated process, but its elastic scattering with nucleons through the exchange of Higgs bosons is highly suppressed due to its pseudo-Goldstone boson nature. The model is therefore free from the constraints arising from direct DM detection experiments. We identify regions of the model parameter space for reproducing the observed DM density compatible with the constraints from the Large Hadron Collider and the indirect DM searches by Fermi-LAT and MAGIC., Comment: 13 pages, 2 figures, updated version accepted for publication in PRD

To address five fundamental shortcomings of the Standard Model (SM) of particle physics and cosmology, we propose a SMART U(1)$_X$ model which is a $U(1)_X \times U(1)_{PQ}$ extension of the SM. The $U(1)_X$ gauge symmetry is a generalization of the well-known $U(1)_{B-L}$ symmetry and $U(1)_{PQ}$ is the global Peccie-Quinn (PQ) symmetry. Three right handed neutrinos are added to cancel $U(1)_X$ related anomalies, and they play a crucial role in understanding the observed neutrino oscillations and explaining the observed baryon asymmetry in the universe via leptogenesis. The PQ symmetry helps resolve the strong CP problem and also provides axion as a compelling dark matter (DM) candidate. The $U(1)_X$ gauge symmetry enables us to implement the inflection-point inflation scenario with $H_{inf} \lesssim 2 \times 10^{7}$ GeV, where $H_{inf}$ is the value of Hubble parameter during inflation. This allows us to overcome a potential axion domain wall problem as well as the axion isocurvature problem. The SMART U(1)$_X$ model can be merged with $SU(5)$ as we briefly show., Comment: 18 pages, 2 figures

We explore $t-b-\tau$ Yukawa unification (YU) in a supersymmetric $SU(4)_c \times SU(2)_L \times SU(2)_R $ model without imposing a discrete left-right (L-R) symmetry. A number of interesting solutions that are compatible with $t-b-\tau$ YU, LSP neutralino dark matter (DM), and LHC and other experimental constraints are identified. In particular, they include gluino-neutralino and stau-neutralino co-annihilation scenarios, where the NLSP gluino mass can range from 1-3 TeV. Higgsino-like dark matter solutions are also identified for which gluino masses can approach 5 TeV or so. This scenario will be tested at LHC Run-3 and its future upgrades.

We explore proton decay in a class of realistic supersymmetric flipped $SU(5)$ models supplemented by a $U(1)_R$ symmetry which plays an essential role in implementing hybrid inflation. Two distinct neutrino mass models, based on inverse seesaw and type I seesaw, are identified, with the latter arising from the breaking of $U(1)_R$ by nonrenormalizable superpotential terms. Depending on the neutrino mass model an appropriate set of intermediate scale color triplets from the Higgs superfields play a key role in proton decay channels that include $p \rightarrow (e^{+},\mu^+)\, \pi^0$, $p \rightarrow ( e^+,\mu^{+})\, K^0 $, $p \rightarrow \overline{\nu}\, \pi^{+}$, and $p \rightarrow \overline{\nu}\, K^+ $. We identify regions of the parameter space that yield proton lifetime estimates which are testable at Hyper-Kamiokande and other next generation experiments. We discuss how gauge coupling unification in the presence of intermediate scale particles is realized, and a $Z_4$ symmetry is utilized to show how such intermediate scales can arise in flipped $SU(5)$. Finally, we compare our predictions for proton decay with previous work based on $SU(5)$ and flipped $SU(5)$., Comment: 31 pages, 8 figures, JHEP published version [the analysis of second neutrino mass model has been corrected with few other minor changes]

We consider magnetic monopoles and strings that appear in non-supersymmetric $SO(10)$ and $E_6$ grand unified models paying attention to gauge coupling unification and proton decay in a variety of symmetry breaking schemes. The dimensionless string tension parameter $G\mu$ spans the range $10^{-6}-10^{-30}$, where $G$ is Newton's constant and $\mu$ is the string tension. We show how intermediate scale monopoles with mass $\sim 10^{13}-10^{14}$ GeV and flux $\lesssim 2.8\times 10^{-16}$ ${\mathrm{cm}^{-2}\mathrm{s}^{-1}\mathrm{sr}^{-1}}$, and cosmic strings with $G\mu \sim 10^{-11}-10^{-10}$ survive inflation and are present in the universe at an observable level. We estimate the gravity wave spectrum emitted from cosmic strings taking into account inflation driven by a Coleman-Weinberg potential. The tensor-to-scalar ratio $r$ lies between $0.06$ and $0.003$ depending on the details of the inflationary scenario., Comment: 38 pages, 9 figures, Published version

We consider a class of SUSY models in which the MSSM gauge group is supplemented with a gauged $U(1)_{B-L}$ symmetry and a global $U(1)_{R}$ symmetry. This extension introduces only electrically neutral states, and the new SUSY partners effectively double the number of states in the neutralino sector that now includes a blino (from $B-L$) and singlino from a gauge singlet superfield. If the DM density is saturated by a LSP neutralino, the model yields quite a rich phenomenology depending on the DM composition. The LSP relic density constraint provides a lower bound on the stop and gluino masses of about 3 TeV and 4 TeV respectively, which is testable in the near future collider experiments such as HL-LHC. The chargino mass lies between 0.24 TeV and about 2.0 TeV, which can be tested based on the allowed decay channels. We also find $m_{\tilde{\tau}_{1}}\gtrsim 500$ GeV, and $m_{\tilde{e}},m_{\tilde{\mu}},m_{\tilde{\nu}^{S,P}} \gtrsim 1$ TeV. We identify chargino-neutralino coannihilation processes in the mass region $0.24 \,{\rm TeV} \lesssim m_{\tilde{\chi}_{1}^{0}}\approx m_{\tilde{\chi}_{1}^{\pm}}\lesssim 1.5$ TeV, and also coannihilation processes involving stau, selectron, smuon and sneutrinos for masses around 1 TeV. In addition, $A_{2}$ resonance solutions are found around 1 TeV, and $H_{2}$ and $H_{3}$ resonance solutions are also shown around 0.5 TeV and 1 TeV . Some of the $A_{2}$ resonance solutions with $\tan\beta \gtrsim 20$ may be tested by the $A/H\rightarrow \tau^{+}\tau^{-}$ LHC searches. While the relic density constraint excludes the bino-like DM, it is still possible to realize higgsino, singlino and blino-like DM for various mass scales. We show that all these solutions will be tested in future direct detection experiments such as LUX-Zeplin and Xenon-nT., Comment: 23 pages,4 figures

We discuss proton decay in a recently proposed model of supersymmetric hybrid inflation based on the gauge symmetry $SU(4)_c \times SU(2)_L \times SU(2)_R$. A $U(1)\, R$ symmetry plays an essential role in realizing inflation as well as in eliminating some undesirable baryon number violating operators. Proton decay is primarily mediated by a variety of color triplets from chiral superfields, and it lies in the observable range for a range of intermediate scale masses for the triplets. The decay modes include $p \rightarrow e^{+}(\mu^+) + \pi^0$, $p \rightarrow \bar{\nu} + \pi^{+}$, $p \rightarrow K^0 + e^+(\mu^{+})$, and $p \rightarrow K^+ + \bar{\nu}$, with a lifetime estimate of order $10^{34}-10^{36}$ yrs and accessible at Hyper-Kamiokande and future upgrades. The unification at the Grand Unified Theory (GUT) scale $M_{\rm GUT}$ ($\sim 10^{16}$ GeV) of the Minimal Supersymmetric Standard Model (MSSM) gauge couplings is briefly discussed., Comment: Version-2: 20 pages, 7 figures, version published in JHEP

We explore possible signatures for charged lepton flavour violation (LFV), sparticle discovery at the LHC and dark matter (DM) searches in grand unified theories (GUTs) based on SU(5), flipped SU(5) (FSU(5)) and SU(4)×SU(2)×SU(2) (4-2-2). We assume that soft supersymmetry-breaking terms preserve the group symmetry at some high input scale, and focus on the non-universal effects on different matter representations generated by gauge interactions at lower scales, as well as the charged LFV induced in Type-1 see-saw models of neutrino masses. We identify the different mechanisms that control the relic DM density in the various GUT models, and contrast their LFV and LHC signatures. The SU(5) and 4-2-2 models offer good detection prospects both at the LHC and in LFV searches, though with different LSP compositions, and the SU(5) and FSU(5) models offer LFV within the current reach. The 4-2-2 model allows chargino and gluino coannihilations with neutralinos, and the former offer good detection prospects for both the LHC and LFV, while gluino coannihilations lead to lower LFV rates. Our results indicate that LFV is a powerful tool that complements LHC and DM searches, providing significant insights into the sparticle spectra and neutrino mass parameters in different models.

Motivated by the recently proposed Trans-Planckian Censorship Conjecture (TCC), we propose a gauged $B-L$ model of inflection-point inflation with axion dark matter. The Hubble scale during inflation ($H_{\rm inf}$) satisfies the TCC bound of $H_{\rm inf} \lesssim 1$ GeV, the axion dark matter scenario is free from the axion domain wall and isocurvature problems, and the axion decay constant can be larger than $10^{12}$ GeV. The seesaw mechanism is automatically incorporated in the model and the observed baryon asymmetry of the universe can be reproduced via resonant leptogenesis., Comment: 6 pages, 2 figures, revised Section V

A realistic tribrid model of sneutrino inflation is constructed in an $R$-symmetric $SU(5)$ grand unified theory (GUT). To avoid the monopole problem, a pseudosmooth inflationary trajectory is generated with the help of an additional $Z_5$ symmetry which is broken during and after inflation. The predictions of inflationary parameters are made at the central value of the scalar spectral index, $n_s =0.968$. The largest possible value of the tensor to scalar ratio, $r\lesssim 0.0027$, is obtained with sub-Planckian field values ($\lesssim m_P$). A successful realization of reheating and leptogenesis is achieved by avoiding the gravitino problem with a reheat temperature as low as $10^6$ GeV. The predicted range of the gauge symmetry breaking scale, $ 5 \times 10^{16} \lesssim M/\text{GeV} \lesssim 5 \times 10^{17}$, turns out to be somewhat larger than the typical GUT scale. With additional vector-like families, a successful gauge coupling unification is achieved by avoiding the no-go theorem related to $R$-symmetric $SU(5)$ GUT., Comment: 18 pages, 8 figures, JCAP published version

We propose a simple non-supersymmetric grand unified theory (GUT) based on the gauge group $SO(10) \times U(1)_\psi$. The model includes 3 generations of fermions in ${\bf 16}$ ($+1$), ${\bf 10}$ ($-2$) and ${\bf 1}$ ($+4$) representations. The ${\bf 16}$-plets contain Standard Model (SM) fermions plus right-handed neutrinos, and the ${\bf 10}$-plet and the singlet fermions are introduced to make the model anomaly-free. Gauge coupling unification at $M_{GUT} \simeq 5 \times 10^{15}-10^{16}$ GeV is achieved by including an intermediate Pati-Salam breaking at $M_{I} \simeq 10^{12}-10^{11}$ GeV, which is a natural scale for the seesaw mechanism. For $M_{I} \simeq 10^{12}-10^{11}$, proton decay will be tested by the Hyper-Kamiokande experiment. The extra fermions acquire their masses from $U(1)_\psi$ symmetry breaking, and a $U(1)_\psi$ Higgs field drives a successful inflection-point inflation with a low Hubble parameter during inflation, $H_{inf} \ll M_{I}$. Hence, cosmologically dangerous monopoles produced from $SO(10)$ and PS breakings are diluted away. The reheating temperature after inflation can be high enough for successful leptogenesis. With the Higgs field contents of our model, a ${\bf Z}_2$ symmetry remains unbroken after GUT symmetry breaking, and the lightest mass eigenstate among linear combinations of the ${\bf 10}$-plet and the singlet fermions serves as a Higgs-portal dark matter (DM). We identify the parameter regions to reproduce the observed DM relic density while satisfying the current constraint from the direct DM detection experiments. The present allowed region will be fully covered by the future direct detection experiments such as LUX-ZEPLIN DM experiment. In the presence of the extra fermions, the SM Higgs potential is stabilized up to $M_{I}$., Comment: 25 pages, 5 figures, new references added

We discuss the gluino mass in the CMSSM and Nonuniversal Gaugino Mass Models (NUGM) frameworks in light of the results from the current LHC and Dark Matter experiments. We probe the gluino mass scales by considering its decay modes into stop and top quarks, $\tilde{g}\rightarrow \tilde{t}_{1}t$ and $\tilde{g}\rightarrow \bar{t}t\tilde{\chi}_{1}^{0}$, where $\tilde{t}_{1}t$ represents both $\tilde{t}_{1}\bar{t}$ and $\tilde{t}_{1}^{*}t$. The region with $m_{\tilde{g}} \lesssim 2$ TeV is excluded up to $68\%$ CL in the CMSSM if the gluino decays into a stop and top quark, while the $95\%$ CL exclusion requires $m_{\tilde{g}}\gtrsim 1.9$ TeV. Such exclusion bounds on the gluino mass more or less overlap with the current LHC results. The decay mode $\tilde{g}\rightarrow \bar{t}t\tilde{\chi}_{1}^{0}$ may take over if $\tilde{g}\rightarrow \tilde{t}_{1}t$ is not allowed. One can probe the gluino mass in this case up to about 1.5 TeV with $68\%$ CL in the CMSSM, and about 1.4 TeV with $95\%$ CL. A similar analyses in the NUGM framework yield exclusion curves for the gluino mass $m_{\tilde{g}}\gtrsim 2.1$ TeV at 14 TeV for both decay modes of the gluino under consideration. We also show that increasing the center of mass energy to 27 TeV can probe the gluino mass up to about 3 TeV through its decay mode into stop and top quark. The Dark Matter constraints are not very severe in the framework of NUGM, and they allow solutions with $m_{\tilde{g}},m_{\tilde{t}} \gtrsim 1$ TeV. In addition, with NUGM the LSP neutralino can coannihilate with gluino and/or stop for $m_{\tilde{g}},m_{\tilde{t}}\approx m_{\tilde{\chi}_{1}^{0}} \in [0.9-1.5]$ TeV. The 100 TeV FCC collider can probe the gluino masses up to about 6 TeV with $36.1~fb^{-1}$ integrated luminosity. We also find that the decay $\tilde{g}\rightarrow \tilde{t}t$ can indirectly probe the stop mass up to about 4 TeV.

The gauge symmetry $SU(5) \times U(1)_\chi$ is the unique maximal subgroup of SO(10) which retains manifest unification at $M_{GUT}$ of the Standard Model gauge couplings, especially if low scale supersymmetry is present. The spontaneous breaking of $U(1)_\chi$ at some intermediate scale leaves unbroken a $Z_2$ symmetry which is precisely `matter' parity. This yields a stable supersymmetric dark matter particle as well as topologically stable cosmic strings. Motivated by the weak gravity conjecture we impose unification of $SU(5)$ and $U(1)_\chi$ at an ultraviolet cutoff $\Lambda \sim \alpha_\Lambda ^{1/2} M_{P} \approx 5 \times 10^{17}$ GeV, where $\alpha_\Lambda$ denotes the $SU(5)$ gauge coupling at $\Lambda$ and $M_P \approx 2.4 \times 10^{18}$ GeV is the reduced Planck Scale. The impact of dimension five operators suppressed by $\Lambda$ on gauge coupling unification, proton lifetime estimates and $b-\tau$ Yukawa unification is discussed. In particular, the gauge boson mediated proton decay into $e^+\pi^0$ can lie within the $2-\sigma$ sensitivity of HyperKamiokande. We also discuss how the intermediate scale strings may survive inflation while the $SU(5)$ monopoles are inflated away. The unbroken $Z_2$ symmetry provides an intriguing link between dark matter, black holes carrying `quantum hair' and cosmic strings., Comment: 6 pages, 6 figures

We show that if global lepton number symmetry is spontaneously broken in a postinflation epoch, then it can lead to the formation of cosmological domain walls. This happens in the well-known >Majoron paradigm> for neutrino mass generation. We propose some realistic examples that allow spontaneous lepton number breaking to be safe from such domain walls.