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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: 22 pages, 6 figures, 1 table, matches version accepted in JCAP

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 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.

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

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 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.

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 $G \mu\sim 10^{-6}$, 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. 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 $10^{36}-10^{37}$ yrs., Comment: Revised version accepted for publication in JCAP

Composite topological structures such as superheavy "quasi-stable strings" (QSS) and "walls bounded by strings" (WBS) 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 evidence 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 walls arise 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. The Bayes factors for QSS and WBS relative to the inspiraling supermassive black hole binaries are estimated to be about 60 and 30 respectively, which are comparable with that of metastable strings and cosmic superstrings., Comment: 6 pages, 1 table, 4 captioned figures, improved results with Bayesian statistics and Bayes factors, matches version published in PRD

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, published version

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

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

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 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, published version

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 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 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

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 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, published version

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

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 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 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 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

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 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 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

The early stages of the universe evolution are discussed according to the hot big bang model and the grand unified theories. The shortcomings of big bang are summarized and their resolution by inflationary cosmology is sketched. Cosmological inflation, the subsequent oscillation and decay of the inflaton field, and the resulting reheating of the universe are studied in some detail. The density perturbations produced by inflation and the temperature fluctuations of the cosmic microwave background radiation are introduced. Baryogenesis via non-thermal leptogenesis is analyzed and dark energy and matter in the universe are presented. Quantum gravity and string theory are very briefly introduced. The problem of initial conditions for inflation is discussed in the light of string theory and the possibly detectable primordial gravity waves from inflation are mentioned., Comment: 23 pages, talk presented in the "Corfu Summer Institute 2019: School and Workshops on Elementary Particle Physics and Gravity (CORFU2019)", 31 August - 25 September 2019, Corfu, Greece, to appear in the proceedings. arXiv admin note: text overlap with arXiv:hep-ph/0607032, arXiv:hep-ph/0204294, arXiv:hep-ph/0111328

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

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 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 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

The early stages of the universe evolution are discussed according to the hot big bang model and the grand unified theories. The shortcomings of big bang are summarized and their resolution by inflationary cosmology is sketched. Cosmological inflation, the subsequent oscillation and decay of the inflaton field, and the resulting reheating of the universe are studied in some detail. The density perturbations produced by inflation and the temperature fluctuations of the cosmic microwave background radiation are introduced. Baryogenesis via non-thermal leptogenesis is analyzed and dark energy and matter in the universe are presented. Quantum gravity and string theory are very briefly introduced. The problem of initial conditions for inflation is discussed in the light of string theory and the possibly detectable primordial gravity waves from inflation are mentioned., Comment: 23 pages, talk presented in the "Corfu Summer Institute 2019: School and Workshops on Elementary Particle Physics and Gravity (CORFU2019)", 31 August - 25 September 2019, Corfu, Greece, to appear in the proceedings. arXiv admin note: text overlap with arXiv:hep-ph/0607032, arXiv:hep-ph/0204294, arXiv:hep-ph/0111328

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

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

The early stages of the universe evolution are discussed according to the hot big bang model and the grand unified theories. The shortcomings of big bang are summarized and their resolution by inflationary cosmology is sketched. Cosmological inflation, the subsequent oscillation and decay of the inflaton field, and the resulting reheating of the universe are studied in some detail. The density perturbations produced by inflation and the temperature fluctuations of the cosmic microwave background radiation are introduced. Baryogenesis via non-thermal leptogenesis is analyzed and dark energy and matter in the universe are presented. Quantum gravity and string theory are very briefly introduced. The problem of initial conditions for inflation is discussed in the light of string theory and the possibly detectable primordial gravity waves from inflation are mentioned., Comment: 23 pages, talk presented in the "Corfu Summer Institute 2019: School and Workshops on Elementary Particle Physics and Gravity (CORFU2019)", 31 August - 25 September 2019, Corfu, Greece, to appear in the proceedings. arXiv admin note: text overlap with arXiv:hep-ph/0607032, arXiv:hep-ph/0204294, arXiv:hep-ph/0111328

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

We show that if global lepton number symmetry is spontaneously broken in a post inflation 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 which allow spontaneous lepton number breaking to be safe from such domain walls., Comment: 8 pages, References added, Discussion on Domain Wall Problem Expanded, Conclusions Unchanged, Version Published in Phys. Rev. Lett

We show that if global lepton number symmetry is spontaneously broken in a post inflation 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 which allow spontaneous lepton number breaking to be safe from such domain walls., Comment: 8 pages, References added, Discussion on Domain Wall Problem Expanded, Conclusions Unchanged, Version Published in Phys. Rev. Lett

It is shown that, in supergravity models of inflation where the gauge kinetic function of a gauge field is modulated by the inflaton, we can obtain a new inflationary attractor solution, in which the roll-over of the inflaton suffers additional impedance due to the vector field backreaction. As a result, directions of the scalar potential which, due to strong Kaehler corrections, become too steep and curved to normally support slow-roll inflation can now naturally do so. This solves the infamous eta-problem of inflation in supergravity and also keeps the spectral index of the curvature perturbation mildly red despite eta of order unity. This mechanism is applied to a model of hybrid inflation in supergravity with a generic Kaehler potential. The spectral index of the curvature perturbation is found to be 0.97 - 0.98, in excellent agreement with data. The gauge field can act as vector curvaton generating statistical anisotropy in the curvature perturbation. However, this anisotropy could be possibly observable only if the gauge coupling constant is unnaturally small., Comment: 10 pages, talk given at the International Workshop on Grand Unified Theories (GUT2012), Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, Japan, March 15-17, 2012 (to appear in the proceedings)

It is shown that, when the inflaton field modulates the gauge kinetic function of the gauge fields in supergravity realisations of inflation, the dynamic backreaction leads to a new inflationary attractor solution, in which the inflaton’s variation suffers additional impedance. As a result, slow-roll inflation can naturally occur along directions of the scalar potential which would be too steep and curved to support it otherwise. This provides a generic solution to the infamous eta-problem of inflation in supergravity. Moreover, it is shown that, in the new inflationary attractor, the spectral index of the generated curvature perturbations is kept mildly red despite eta of order unity. The above findings are applied to a model of hybrid inflation in supergravity with a generic K¨ahler potential. The spectral index of the generated curvature perturbations is found to be 0.97–0.98, in excellent agreement with observations. The gauge field can play the role of the vector curvaton after inflation but observable statistical anisotropy requires substantial tuning of the gauge coupling.

It is shown that, in supergravity models of inflation where the gauge kinetic function of a gauge field is modulated by the inflaton, we can obtain a new inflationary attractor solution, in which the roll-over of the inflaton suffers additional impedance due to the vector field backreaction. As a result, directions of the scalar potential which, due to strong Kaehler corrections, become too steep and curved to normally support slow-roll inflation can now naturally do so. This solves the infamous eta-problem of inflation in supergravity and also keeps the spectral index of the curvature perturbation mildly red despite eta of order unity. This mechanism is applied to a model of hybrid inflation in supergravity with a generic Kaehler potential. The spectral index of the curvature perturbation is found to be 0.97 - 0.98, in excellent agreement with data. The gauge field can act as vector curvaton generating statistical anisotropy in the curvature perturbation. However, this anisotropy could be possibly observable only if the gauge coupling constant is unnaturally small., Comment: 10 pages, talk given at the International Workshop on Grand Unified Theories (GUT2012), Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, Japan, March 15-17, 2012 (to appear in the proceedings)

It is shown that, when the inflaton field modulates the gauge kinetic function of the gauge fields in supergravity realisations of inflation, the dynamic backreaction leads to a new inflationary attractor solution, in which the inflaton’s variation suffers additional impedance. As a result, slow-roll inflation can naturally occur along directions of the scalar potential which would be too steep and curved to support it otherwise. This provides a generic solution to the infamous eta-problem of inflation in supergravity. Moreover, it is shown that, in the new inflationary attractor, the spectral index of the generated curvature perturbations is kept mildly red despite eta of order unity. The above findings are applied to a model of hybrid inflation in supergravity with a generic K¨ahler potential. The spectral index of the generated curvature perturbations is found to be 0.97–0.98, in excellent agreement with observations. The gauge field can play the role of the vector curvaton after inflation but observable statistical anisotropy requires substantial tuning of the gauge coupling.

It is shown that, in supergravity models of inflation where the gauge kinetic function of a gauge field is modulated by the inflaton, we can obtain a new inflationary attractor solution, in which the roll-over of the inflaton suffers additional impedance due to the vector field backreaction. As a result, directions of the scalar potential which, due to strong Kaehler corrections, become too steep and curved to normally support slow-roll inflation can now naturally do so. This solves the infamous eta-problem of inflation in supergravity and also keeps the spectral index of the curvature perturbation mildly red despite eta of order unity. This mechanism is applied to a model of hybrid inflation in supergravity with a generic Kaehler potential. The spectral index of the curvature perturbation is found to be 0.97 - 0.98, in excellent agreement with data. The gauge field can act as vector curvaton generating statistical anisotropy in the curvature perturbation. However, this anisotropy could be possibly observable only if the gauge coupling constant is unnaturally small., Comment: 10 pages, talk given at the International Workshop on Grand Unified Theories (GUT2012), Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, Japan, March 15-17, 2012 (to appear in the proceedings)

It is shown that, when the inflaton field modulates the gauge kinetic function of the gauge fields in supergravity realisations of inflation, the dynamic backreaction leads to a new inflationary attractor solution, in which the inflaton's variation suffers additional impedance. As a result, slow-roll inflation can naturally occur along directions of the scalar potential which would be too steep and curved to support it otherwise. This provides a generic solution to the infamous eta-problem of inflation in supergravity. Moreover, it is shown that, in the new inflationary attractor, the spectral index of the generated curvature perturbations is kept mildly red despite eta of order unity. The above findings are applied to a model of hybrid inflation is supergravity with a generic Kaehler potential. The spectral index of the generated curvature perturbations is found to be 0.97 - 0.98, in excellent agreement with observations. The gauge field can play the role of the vector curvaton after inflation but observable statistical anisotropy requires substantial tuning of the gauge coupling., Comment: 25 pages. Published in JCAP. Minor corrections. References added

It is shown that, when the inflaton field modulates the gauge kinetic function of the gauge fields in supergravity realisations of inflation, the dynamic backreaction leads to a new inflationary attractor solution, in which the inflaton's variation suffers additional impedance. As a result, slow-roll inflation can naturally occur along directions of the scalar potential which would be too steep and curved to support it otherwise. This provides a generic solution to the infamous eta-problem of inflation in supergravity. Moreover, it is shown that, in the new inflationary attractor, the spectral index of the generated curvature perturbations is kept mildly red despite eta of order unity. The above findings are applied to a model of hybrid inflation is supergravity with a generic Kaehler potential. The spectral index of the generated curvature perturbations is found to be 0.97 - 0.98, in excellent agreement with observations. The gauge field can play the role of the vector curvaton after inflation but observable statistical anisotropy requires substantial tuning of the gauge coupling., Comment: 25 pages. Published in JCAP. Minor corrections. References added

It is shown that, when the inflaton field modulates the gauge kinetic function of the gauge fields in supergravity realisations of inflation, the dynamic backreaction leads to a new inflationary attractor solution, in which the inflaton's variation suffers additional impedance. As a result, slow-roll inflation can naturally occur along directions of the scalar potential which would be too steep and curved to support it otherwise. This provides a generic solution to the infamous eta-problem of inflation in supergravity. Moreover, it is shown that, in the new inflationary attractor, the spectral index of the generated curvature perturbations is kept mildly red despite eta of order unity. The above findings are applied to a model of hybrid inflation is supergravity with a generic Kaehler potential. The spectral index of the generated curvature perturbations is found to be 0.97 - 0.98, in excellent agreement with observations. The gauge field can play the role of the vector curvaton after inflation but observable statistical anisotropy requires substantial tuning of the gauge coupling., Comment: 25 pages. Published in JCAP. Minor corrections. References added

We analyze the most salient cosmological features of axions in extensions of the Standard Model with a gauged anomalous extra U(1) symmetry. The model is built by imposing the constraint of gauge invariance in the anomalous effective action, which is extended with Wess-Zumino counterterms. These generate axion-like interactions of the axions to the gauge fields and a gauged shift symmetry. The scalar sector is assumed to acquire a non-perturbative potential after inflation, at the electroweak phase transition, which induces a mixing of the Stuckelberg field of the model with the scalars of the electroweak sector, and at the QCD phase transition. We discuss the possible mechanisms of sequential misalignments which could affect the axions of these models, and generated, in this case, at both transitions. We compute the contribution of these particles to dark matter, quantifying their relic densities as a function of the Stuckelberg mass. We also show that models with a single anomalous U(1) in general do not account for the dark energy, due to the presence of mixed U(1)-SU(3) anomalies., Comment: 29 pages, 5 figures. Revised version, accepted by Phys. Rev. D

We analyze the most salient cosmological features of axions in extensions of the Standard Model with a gauged anomalous extra U(1) symmetry. The model is built by imposing the constraint of gauge invariance in the anomalous effective action, which is extended with Wess-Zumino counterterms. These generate axion-like interactions of the axions to the gauge fields and a gauged shift symmetry. The scalar sector is assumed to acquire a non-perturbative potential after inflation, at the electroweak phase transition, which induces a mixing of the Stuckelberg field of the model with the scalars of the electroweak sector, and at the QCD phase transition. We discuss the possible mechanisms of sequential misalignments which could affect the axions of these models, and generated, in this case, at both transitions. We compute the contribution of these particles to dark matter, quantifying their relic densities as a function of the Stuckelberg mass. We also show that models with a single anomalous U(1) in general do not account for the dark energy, due to the presence of mixed U(1)-SU(3) anomalies., Comment: 29 pages, 5 figures. Revised version, accepted by Phys. Rev. D