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The "new standard cosmology", based on the theory of inflation, has very impressive observational support. I review some outstanding problems of the new cosmology and the global view of the universe -- the multiverse -- that it suggests. I focus in particular on prospects for further observational tests of inflation and of the multiverse., Invited talk at TAUP conference, Rome, July 2009

In this work we analyze how the spectrum of primordial scalar perturbations is modified, within the emergent universe scenario, when a particular version of the Continuous Spontaneous Localization (CSL) model is incorporated as the generating mechanism of initial perturbations, providing also an explanation to the quantum-to-classical transition of such perturbations. On the other hand, a phase of super-inflation, prior to slow-roll inflation, is a characteristic feature of the emergent universe hypothesis. In recent works, it was shown that the super-inflation phase could generically induce a suppression of the temperature anisotropies of the CMB at large angular scales. We study here under what conditions the CSL maintains or modifies these characteristics of the emergent universe and their compatibility with the CMB observations., Comment: 15 pages, 5 figures. Some references added. Version accepted in EPJC

We propose a minimal model that can explain the electroweak scale, neutrino masses, Dark Matter (DM), and successful inflation all at once based on the multicritical-point principle (MPP). The model has two singlet scalar fields that realize an analogue of the Coleman-Weinberg mechanism, in addition to the Standard Model with heavy Majorana right-handed neutrinos. By assuming a $Z_2 $ symmetry, one of the scalars becomes a DM candidate whose property is almost the same as the minimal Higgs-portal scalar DM. In this model, the MPP can naturally realize a saddle point in the Higgs potential at high energy scales. By the renormalization-group analysis, we study the critical Higgs inflation with non-minimal coupling $\xi |H|^2 R$ that utilizes the saddle point of the Higgs potential. We find that it is possible to realize successful inflation even for $\xi=25$ and that the heaviest right-handed neutrino is predicted to have a mass around $10^{14}$ GeV to meet the current cosmological observations. Such a small value of $\xi$ can be realized by the Higgs-portal coupling $\lambda_{SH}\simeq 0.32$ and the vacuum expectation value of the additional neutral scalar $\langle\phi\rangle\simeq 2.7$ TeV, which correspond to the dark matter mass 2.0 TeV, its spin-independent cross section $1.8\times10^{-9}$ pb, and the mass of additional neutral scalar 190 GeV., Comment: 30 pages, 7 figures; Version accepted in EPJC (v2)

Analytic and numerical techniques are presented for computing gravitational production of scalar particles in the limit that the inflaton mass is much larger than the Hubble expansion rate at the end of inflation. These techniques rely upon adiabatic invariants and time modeling of a typical inflaton field which has slow and fast time variation components. A faster computation time for numerical integration is achieved via subtraction of slowly varying components that are ultimately exponentially suppressed. The fast oscillatory remnant results in production of scalar particles with a mass larger than the inflationary Hubble expansion rate through a mechanism analogous to perturbative particle scattering. An improved effective Boltzmann collision equation description of this particle production mechanism is developed. This model allows computation of the spectrum using only adiabatic invariants, avoiding the need to explicitly solve the inflaton equations of motion., 37 pages, 5 figures

Constant-rate inflation, including ultra-slow-roll as a special case, has been widely applied to the formation of primordial black holes with significant deviation from the standard slow-roll conditions at both the growing and decaying phases of the power spectrum. We derive analytic solutions for the curvature perturbations with respect to the late-time scaling dimensions (conformal weights) constrained by the dilatation symmetry of the de Sitter background and show that the continuity of conformal weights across different rolling phases is protected by the adiabatic condition of the inflaton perturbation. The temporal excitation of subleading states (with the next-to-lowest conformal weights), recorded as the "steepest growth" of the power spectrum, is triggered by the entropy production in the transition from slow-roll to constant-rate phases., Comment: 18 + 4 pages, 6 figures; v2: references added, provided entropy production as a criterion for the steepest growth; v3: minor corrections, version matched with publication

The policy debate in Turkey over the impact of interest rate on inflation concerns the question of what policymakers should do when faced with volatile and high inflation. Motivated by this discussion, we provide an empirical analysis by connecting the cost channel to the Phillips relation. Our findings prove the existence of the cost channel. However, other determinants of inflation —labor share of income, prices of imported inputs, and consumption goods —dominate the cost channel in Turkey.

The interactions between spin of fermionic matter and torsion in Einstein-Cartan-Sciama-Kibble (ECSK) theory of gravity provide a repulsive gravitational potential at very dense states of fermionic matter, which prevents the formation of black hole singularities inside the deeper horizon. While the fermionic matter in the black hole is attracted by the black hole at the beginning, after a critical point it is repelled to bounce at a critical high density and then expand into other side of the horizon as a newly created space, which may be considered as a non-singular, closed universe. We constructed the action of these fermions in a black hole with torsion in the framework of ECSK theory of gravity from which the free Dirac action is inferred and the interaction potential is obtained. Also, this scenario naturally solves the flatness and horizon problems of cosmology without introducing finely tuned scalar fields, or more complicated functions of the Ricci scalar R in gravitational action.

We describe a new phenomenon in quantum cosmology: self-organised localisation. When the fundamental parameters of a theory are functions of a scalar field subject to large fluctuations during inflation, quantum phase transitions can act as dynamical attractors. As a result, the theory parameters are probabilistically localised around the critical value and the Universe finds itself at the edge of a phase transition. We illustrate how self-organised localisation could account for the observed near-criticality of the Higgs self-coupling, the naturalness of the Higgs mass, or the smallness of the cosmological constant., 104 pages, 12 figures. v3: Measure problem discussion extended and references added. Version to be published in JHEP

Solid inflation is a cosmological model where inflation is driven by fields which enter the Lagrangian in the same way as body coordinates of a solid matter enter the equation of state, spontaneously breaking spatial translational and rotational symmetry. We construct a simple generalization of this model by adding a scalar field with standard kinetic term to the action. In our model the scalar power spectrum and the tensor-to-scalar ratio do not differ from the ones predicted by the solid inflation qualitatively, if the scalar field does not dominate the solid matter. The same applies also for the size of the scalar bispectrum measured by the non-linearity parameter, although our model allows it to have different shapes. The tensor bispectra predicted by the two models do not differ from each other in the leading order of the slow-roll approximation. In the case when contribution of the solid matter to the stress-energy tensor is much smaller than the contribution from the scalar field, the tensor-to-scalar ratio and the non-linearity parameter are amplified by factors $\epsilon^{-1}$ and $\epsilon^{-2}$ respectively., Comment: 23 pages, 3 figures

In Einstein's Field Equation(EFE) the geometry of the space-time is connected with the matter distribution. The geometry or the gravitational sector deals with classical macroscopic objects involving gravitational units while the matter sector can be better described by quantum theory involving atomic units. It has been argued by Bisabr that there exists an epoch-dependent conversion factor between these two unit systems present in two different conformal frames,i.e. the conformal factor is epoch dependent. We argue that the conformal transformation is a dynamical degree of freedom describing it's possible relevance in inflation in context to the graceful exit problem, dynamics of the cosmological constant {\Lambda} and justify the argument in the light of consequences of Dirac's Large Number hypothesis(LNH)., Comment: 11 Pages, Previously this version appeared as arXiv:2005.09458v2 which was submitted as a replacement work by accident

We search for effective axions with super-Planckian decay constants in type IIB string models. We argue that such axions can be realised as long winding trajectories in complex-structure moduli space by an appropriate flux choice. Our main findings are: The simplest models with aligned winding in a 2-axion field space fail due to a general no-go theorem. However, equally simple models with misaligned winding, where the effective axion is not close to any of the fundamental axions, appear to work to the best of our present understanding. These models have large decay constants but no large monotonic regions in the potential, making them unsuitable for large-field inflation. We also show that our no-go theorem can be avoided by aligning three or more axions. We argue that, contrary to misaligned models, such models can have both large decay constants and large monotonic regions in the potential. Our results may be used to argue against the refined Swampland Distance Conjecture and strong forms of the axionic Weak Gravity Conjecture. It becomes apparent, however, that realising inflation is by far harder than just producing a light field with large periodicity., Comment: 45 pages. v2: minor improvements and added reference

There are unsolved problems related to inflation, gravity, dark matter, dark energy, and the fate of the universe. Some of them can be better answered by assuming the existence of aether and hypoatoms. Both were created during the inflation in the very early universe. While aether forms vacuum, hypoatoms form all observable matter. In vacuum, aether exists between the particle-antiparticle form and the energy form in a dynamic equilibrium: A + A-bar = gamma + gamma, resulting in quantum phenomena and a character of negative pressure. The proposed hypoatom has an antimatter nucleus, with an equal mass of matter particles of aether in its perimeter, so the enigma of missing antimatter does not exist. At hypoatoms, the forward reaction of the aether annihilation dominates. With constant-density dark energy, the annihilation constantly consumes the aether in vacuum, producing a sink flow of aether that warps spacetime, and thus generates gravity and a dark matter halo in the vicinity of massive objects. The hypoatom is believed to be a neutrino n1, with a mass of 5 meV. Based on the hypoatom structure, singularities do not exist inside black holes; their cores are hypoatom stars or neutrino stars. By gaining enough mass, ca. , to exceed neutrino degeneracy pressure, a black hole collapses or annihilates into the singularity, thus turning itself into a white hole or a new Big Bang.

The anomalously large radii of highly-irradiated gaseous exoplanets has long been a mystery. One mechanism suggested as a solution for hot Jupiters is the heating of the deep atmosphere via the vertical advection of potential temperature resulting in an increased internal entropy. Here we intend to explore if this mechanism can also explain the observed brown dwarf radii trend: a general increase in radius with irradiation, with an exception for highly-irradiated brown dwarfs orbiting white dwarfs. We use a 3D GCM, DYNAMICO, to run a series of long-timescale models of the atmospheres of Kepler-13Ab, KELT-1b, and SDSS1411B. These models allow us to explore not only if a stable advective adiabat can develop, but also the associated dynamics. We find that our models fall into two distinct regimes: Kepler-13Ab and KELT-1b both show signs of significant deep heating and hence maintain adiabats that are hotter than 1D models predict. On the other hand, SDSS1411B exhibits a much weaker downward heating profile which not only struggles to heat the interior under ideal conditions, but is highly sensitive to the presence of deep radiative dynamics. We find that the vertical advection of potential temperature by large-scale atmospheric circulations represents a robust mechanism to explain the trend of increasing inflation with irradiation, including the exception for highly irradiated brown dwarfs orbiting white dwarfs. This can be understood as occurring due to the role that increasing rotational influence plays on mid- to-high latitude advective dynamics. Furthermore, when paired with a suitable parametrisation of the outer atmosphere irradiation profile, this mechanism alone could potentially provide a complete explanation for the observed levels of inflation in our brown dwarfs., 20 pages, 11 figures. Accepted for publication in A&A. Updated version with a fixed typo in the vertical enthalpy flux equation

We consider the possibility of extra spinning particles during inflation, focussing on the spin-2 case. Our analysis relies on the well-known fully non-linear formulation of interacting spin-2 theories. We explore the parameter space of the corresponding inflationary Lagrangian and identify regions therein exhibiting signatures within reach of upcoming CMB probes. We provide a thorough study of the early and late-time dynamics ensuring that stability conditions are met throughout the cosmic evolution. We characterise in particular the gravitational wave spectrum and three-point function finding a local-type non-Gaussianity whose amplitude may be within the sensitivity range of both the LiteBIRD and CMB-S4 experiments., 30 pages, 6 figures; v2 -- references added, minor changes, accepted for publication in JCAP

Heavy particles with masses much bigger than the inflationary Hubble scale $H_*$, can get non-adiabatically pair produced during inflation through their couplings to the inflaton. If such couplings give rise to time-dependent masses for the heavy particles, then following their production, the heavy particles modify the curvature perturbation around their locations in a time-dependent and scale non-invariant manner. This results into a non-trivial spatial profile of the curvature perturbation that is preserved on superhorizon scales and eventually generates localized hot or cold spots on the CMB. We explore this phenomenon by studying the inflationary production of heavy scalars and derive the final temperature profile of the spots on the CMB by taking into account the subhorizon evolution, focusing in particular on the parameter space where pairwise hot spots (PHS) arise. When the heavy scalar has an $\mathcal{O}(1)$ coupling to the inflaton, we show that for an idealized situation where the dominant background to the PHS signal comes from the standard CMB fluctuations themselves, a simple position space search based on applying a temperature cut, can be sensitive to heavy particle masses $M_0/H_*\sim\mathcal{O}(100)$. The corresponding PHS signal also modifies the CMB power spectra and bispectra, although the corrections are below (outside) the sensitivity of current measurements (searches)., Comment: 25+5 pages, 9+2 figures

As we know, the inflation models have been considered by researchers in various fields of physics such as cosmology and particle physics for explaining early Universe. According to different conditions and conjectures, there are several types of inflation models. In this article, we want to examine a new condition for the inflation models which is known as the swampland criterion. Therefore, we consider f(R) model that includes a polynomial plus a logarithmic term as $$R+\alpha R^{2}+\beta R^{n}+\gamma R^{2}\log \gamma R$$ . So, by considering the corresponding modified f(R) gravity on the brane, we obtain the modified cosmological parameters such as spectral index, tensor-to-scalar ratio and a number of e-folds. These modified parameters give us the opportunity to test the compatibility of f(R) gravity model with swampland criteria. Finally, by using some figures as well as observable data, we specify the range of modified cosmological parameters.

Oscillons are long-lived, localized, oscillating nonlinear excitations of a real scalar field which can be abundantly produced during preheating after inflation. We give the first $(3+1)$-dimensional simulation for the oscillon formation during preheating with noncanonical kinetic terms, e.g. the Dirac-Born-Infeld form, and find that the formation of oscillons is significantly influenced by the noncanonical effect., Comment: 5 pages, 4 figures; more results added, version accepted for publication in PLB

A problematic feature of low energy scale inflationary models, such as Starobinsky inflation, in a spatially closed universe is the occurrence of a recollapse and a big crunch singularity before inflation can even set in. In a recent work it was shown that this problem can be successfully resolved in loop quantum cosmology for a large class of initial conditions due to a non-singular cyclic evolution and a hysteresis-like phenomena. However, for certain highly unfavorable initial conditions the onset of inflation was still difficult to obtain. In this work, we explore the role of dissipative particle production, which is typical in warm inflation scenario, in the above setting. We find that entropy production sourced by such dissipative effects makes hysteresis-like phenomena stronger. As a result, the onset of inflation is quick in general including for highly unfavorable initial conditions where it fails or is significantly delayed in the absence of dissipative effects. We phenomenologically consider three warm inflation scenarios with distinct forms of dissipation coefficient, and from dynamical solutions and phase space portraits find that the phase space of favorable initial conditions turns out to be much larger than in cold inflation., 19 pages, 12 figures. Discussion revised. References added. To appear in Phys. Rev. D

We study single-field inflationary models with steep step-like features in the potential that lead to the temporary violation of the slow-roll conditions during the evolution of the inflaton. These features enhance the power spectrum of the curvature perturbations by several orders of magnitude at certain scales and also produce prominent oscillatory patterns. We study analytically and numerically the inflationary dynamics. We describe quantitatively the size of the enhancement, as well as the profile of the oscillations, which are shaped by the number and position of the features in the potential. The induced tensor power spectrum inherits the distinctive oscillatory profile of the curvature spectrum and is potentially detectable by near-future space interferometers. The enhancement of the power specrtum by step-like features, though significant, may be insufficient to trigger the production of a sizeable number of primordial black holes if radiation dominates the energy density of the early universe. However, it can result in sufficient black hole production if the universe is dominated by non-relativistic matter. For the latter scenario, we find that deviations from the standard monochromatic profile of the mass spectrum of primordial black holes are possible because of the multiple-peak structure of the curvature power spectrum., 37 pages, 14 figures. Journal Version

In this work, we revisit the non-minimally coupled Higgs Inflation scenario and investigate its observational viability in light of the current Cosmic Microwave Background, Baryon Acoustic Oscillation and type Ia Supernovae data. We explore the effects of the Coleman-Weinberg approximation to the Higgs potential in the primordial universe, connecting the predictions for the Lagrangian parameters at inflationary scales to the electroweak observables through Renormalization Group methods at two-loop order. Initially, we find that electroweak scale measurements may be dissonant to the limits obtained from the cosmological data sets used in the analysis. Specifically, an ≈ 8σ-discrepancy between the inflationary parameters and the value of the Monte Carlo reconstructed top quark mass is found. However, considering the most recent results obtained by the CMS Collaboration from differential cross-section measurements of the top quark production a good agreement is obtained.

In the early universe it is important to take into account quantum effect of the gravity to explain the feature of the inflation. In this paper, we consider the M-theory effective action which consists of 11 dimensional supergravity and (Weyl)$^4$ terms. The equations of motion are solved perturbatively, and the solution describes the inflation-like expansion in 4 dimensional spacetime. Scalar and tensor perturbations around this background are evaluated analytically and their behaviors are investigated numerically. If we assume that these perturbations are constant at the beginning of the inflation, spectral indices for scalar and tensor perturbations become almost scale invariant., Comment: 21 pages, 5 figures, a reference added

We ask the question 'what happens to Bloch waves in gratings synthetically moving at near the speed of light?'. First we define a constant refractive index (CRI) model in which Bloch waves remain well defined as they break the light barrier, then show their dispersion rotating through 360 degrees from negative to positive and back again. Next we introduce the effective medium approximation (EMA) then refine it into a 4-wave model which proves to be highly accurate. Finally using the Bloch waves to expand a pulse of light we demonstrate sudden inflation of pulse amplitude combined with reversal of propagation direction as a luminal grating is turned on., Comment: 11 pages, 5 figures

The BB-mode correlation angular power spectrum of CMB is studied for primordial massive gravitational waves for several inflation models. The comparative study of the angular power spectrum with the joint BICEP2/Keck Array and Planck data suggests further constraint on the lower and upper bounds on the mass of primordial gravitons. Assuming a modified dispersion relation, the mass of primordial graviton is also calculated. The resulting constraint also agrees with other theoretical estimates., Comment: 11 pages, 7 figures

It is shown that the inflationary model is the result of the symmetry of the generalized F(R,T,X,φ)-cosmological model using the Noether symmetry. It leads to a solution, a particular case of which is Starobinsky’s cosmological model. It is shown that even in the more particular case of cosmological models F(R,X,φ) and F(T,X,φ) the Monge–Ampère equation is still obtained, one of the solutions including the Starobinsky model. For these models, it is shown that one can obtain both power-law and exponential solutions for the scale factor from the Euler–Lagrange equations. In this case, the scalar field φ has similar time dependences, exponential and exponential. The resulting form of the Lagrangian of the model allows us to consider it as a model with R2 or X2. However, it is also shown that previously less studied models with a non-minimal relationship between R and X are important, as one of the possible models. It is shown that in this case the power-law model can have a limited evolutionary period with a negative value of the kinetic term.

It has been a half-decade since the first direct detection of gravitational waves, which signifies the coming of the era of the gravitational-wave astronomy and gravitational-wave cosmology. The increasing number of the detected gravitational-wave events has revealed the promising capability of constraining various aspects of cosmology, astronomy, and gravity. Due to the limited space in this review article, we will briefly summarize the recent progress over the past five years, but with a special focus on some of our own work for the Key Project ``Physics associated with the gravitational waves'' supported by the National Natural Science Foundation of China. In particular, (1) we have presented the mechanism of the gravitational-wave production during some physical processes of the early Universe, such as inflation, preheating and phase transition, and the cosmological implications of gravitational-wave measurements; (2) we have put constraints on the neutron star maximum mass according to GW170817 observations; (3) we have developed a numerical relativity algorithm based on the finite element method and a waveform model for the binary black hole coalescence along an eccentric orbit., v1, 93 pages, 18 figures, prepared as a status review of project report for Sci. China Phys. Mech. Astron.; v2, 95 pages, minor revision, references added, accepted for publication in Sci. China Phys. Mech. Astron; v3, to match the published version

The work presented in this paper aims to study the inflationary cosmology of [Formula: see text] gravity where [Formula: see text] by two models of Dark Energy (DE), namely Variable Generalized Chaplygin Gas (VGCG) and the Nojiri–Odintsov Holographic Dark Energy. The reconstruction has been carried out in the absence as well as presence of viscosity. The viscous pressure is considered to be [Formula: see text], where [Formula: see text] and [Formula: see text] is the Hubble parameter. In viscous and nonviscous scenarios, the reconstruction has been carried out for power law scale factor and bounce scale factor. For the specific range of cosmic time [Formula: see text], the quintessence and quintom behavior are observed for the equation of state parameters. The slow roll parameters have been studied for both the cases in nonviscous scenario and for the case, namely bounce scale factor for VGCG of nonviscous scenario, we have found that there is a scope of exit from inflation. Furthermore, constraints have been deduced to study the presence of singularity. Finally, the [Formula: see text] gravity is reconstructed as a function of cosmic time [Formula: see text] and is found to stay at positive level for a range of cosmic time [Formula: see text].

An alternative scenario about the phenomenology of primordial Universe is k-inflation. According to this concept, inflation can be achieved by nonstandard kinetic term of scalar field, namely the inflaton. In this project we focus on k-essence models in the presence of a higher order and a linear kinetic term. Furthermore, the inflationary phenomenology with a Dirac-Born-Infeld scalar field is briefly examined, which arises from quantum theories of gravity such as superstring theory. Our approach about the inflationary era is that it can be described in the context of Einstein's gravity involving quantum corrections such as the Chern-Simons string inspired parity violating gravitational term. The equations of motion namely, the Friedmann equation, the Raychadhuri equation and the Klein-Gordon equation for an expanding background are extracted from the gravitational action utilizing the variational principle. The consequential system of differential equations with respect to Hubble's parameter and the inflaton field was quite perplexed in order to be solved with an analytic way. Therefore, the slow-roll conditions during inflationary era were imposed and terms with minor numerically contribution were neglected. From the overall phenomenological analysis it is proved that, models with exotic kinetic terms can generate viable results in consistency with the latest Planck data. Finally, the presence of Chern-Simons quantum corrections shifts the primordial spectral tensor index to blue. Even though blue gravitational waves have yet to be observed, if detected, compatibility with the aforementioned theory can be achieved., Accepted in International Journal of Modern Physics A. arXiv admin note: text overlap with arXiv:2107.09457

In this paper we study two different cases of inhomogeneous EOS of the form p_d = \omega(t)\rho_d+w_1 f(H, t) . We derive the energy density of dark fluid and dark matter component for both the cases. Further we calculate the evolution of energy density, gravitational constant and cosmological constant. We also explore the finite time singularity and thermodynamic stability conditions for the two cases of EOS. Finally, we discuss the thermodynamics of inhomogeneous EOS with the derivation of internal energy, Temperature and entropy and also show that all the stability conditions are satisfied for the two cases of EOS, Comment: 28 pages, 26 figures

Primordial blackholes formed in the early Universe via gravitational collapse of over-dense regions may contribute a significant amount to the present dark matter relic density. Inflation provides a natural framework for the production mechanism of primordial blackholes. For example, single field inflation models with a fine-tuned scalar potential may exhibit a period of ultra-slow roll, during which the curvature perturbation may be enhanced to become seeds of the primordial blackholes formed as the corresponding scales reenter the horizon. In this work, we propose an alternative mechanism for the primordial blackhole formation. We consider a model in which a scalar field is coupled to the Gauss-Bonnet term and show that primordial blackholes may be seeded when a scalar potential term and the Gauss-Bonnet coupling term are nearly balanced. Large curvature perturbation in this model not only leads to the production of primordial blackholes but it also sources gravitational waves at the second order. We calculate the present density parameter of the gravitational waves and discuss the detectability of the signals by comparing them with sensitivity bounds of future gravitational wave experiments., Comment: v1: 9 pages, 3 figures; v2: 10 pages, 3 figures, references updated, version accepted for publication in PRD

We embed natural inflation in an explict string theory model and derive observables in cosmology. We achieve this by compactifying the type IIB string on a Calabi-Yau orientifold, stabilizing moduli via the Large Volume Scenario, and configuring axions using D7-brane stacks. In order to obtain a large effective decay constant, we employ the Kim-Nilles-Peloso alignment mechanism, with the required multiple axions arising naturally from anisotropic bulk geometries. The bulk volumes, and hence the axion decay constants, are stabilized by generalized one-loop corrections and subject to various conditions: the K\"ahler cone condition on the string geometry; the convex hull condition of the weak gravity conjecture; and the constraint from the power spectrum of scalar perturbations. We find that all constraints can be satisfied in a geometry with relatively small volume and thus heavy bulk axion mass. We also covariantize the convex hull condition for the axion-dilaton-instanton system and verify the normalization of the extremal bound., Comment: 54 pages, 8 figures

In this paper, we study a constant-roll inflationary model in the context of brane-world cosmology caused by a quintessence scalar field for warm inflation with a constant dissipative parameter [Formula: see text]. We determine the analytical solution for the Friedmann equation coupled to the equation of motion of the scalar field. The evolution of the primordial scalar and tensor perturbations is also studied using the modified Langevin equation. To check the viability of the model, we use numerical approaches and plot some figures. Our results for the scalar spectral index and the tensor-to-scalar ratio show good consistency with observations.

We consider a short rollercoaster cosmology based on two stages of monodromy inflation separated by a stage of matter domination, generated after the early inflaton falls out of slow roll. If the first stage is controlled by a flat potential, V∼ϕp with p<1 and lasts N∼30–40 e-folds, the scalar and tensor perturbations at the largest scales will fit the CMB perfectly, and produce relic gravity waves with 0.02≲r≲0.06, which can be tested by LiteBIRD and CMB-S4 experiments. If in addition the first inflaton is strongly coupled to a hidden sector U(1), there will be an enhanced production of vector fluctuations near the end of the first stage of inflation. These modes convert rapidly to tensors during the short epoch of matter domination, and then get pushed to superhorizon scales by the second stage of inflation, lasting another 20–30 e-folds. This band of gravity waves is chiral, arrives today with wavelengths in the range of 108 km, and with amplitudes greatly enhanced compared to the long wavelength CMB modes by vector sources. It is therefore accessible to LISA. Thus our model presents a rare early universe theory predicting several simultaneous signals testable by a broad range of gravity wave searches in the very near future.

We investigate the enhancement of the curvature perturbations in a single-field slow-roll inflation with a spectator scalar field kinetically coupled to the inflaton. The coupling term with a periodic function of inflaton triggers the exponential growth of the spectator field perturbations, which indirectly amplifies the curvature perturbations to produce a sizable abundance of primordial black holes (PBHs). This scenario is found to be insensitive to the inflationary background. We study two distinct populations of the stochastic gravitational wave background (SGWB) produced in this scenario, i.e., induced by the scalar perturbations during the inflationary era and the radiation-dominated era, respectively. With the appropriate choices of parameter space, we consider two PBH mass windows of great interest. One is PBHs of masses $\mathcal{O}(10^{-12})M_\odot$ that can be a vital component of dark matter, and the predicted total energy spectrum of SGWB shows a unique profile and is detectable by LISA and Taiji. The other is PBHs of masses $\mathcal{O}(10)M_\odot$ which can provide consistent explanation for the LIGO-Virgo events. More interestingly, the predicted gravitational wave signal from the radiation-dominated era may account for the NANOGrav results., Comment: 22 pages, 4 figures, 1 table

In this paper, we show that a smooth dynamic evolution from an initial unstable de Sitter stage to the standard radiation phase can analytically be described by a dominant noncanonical scalar field. For all practical purposes, at the end of the vacuum decaying process, the remaining potential energy density is completely stored in the kinetic part of the field satisfying the radiation equation of state. In this model, the early universe is nonsingular, free of horizon and different from many inflationary variants none post-inflationary reheating is required since the formation of the thermal bath is concomitant with inflation. The thermodynamic evolution of the thermal bath is determined. It is also shown that the resulting noncanonical cosmology can be rigorously interpreted as a dynamical [Formula: see text]-model (vacuum fluid) whose spontaneous decaying process into radiation may be the origin of the primeval thermal bath.

Models of inflationary cosmology admit a choice of the metric for which the geometry of homogeneous isotropic solutions becomes flat Minkowski space in the infinite past. In this primordial flat frame all mass scales vanish in the infinite past and quantum scale symmetry is realized. The cosmological evolution is dominantly described by the slow increase of a scalar field which sets the scale of all masses. We construct the primordial flat frame for standard models of inflation as Starobinsky inflation or chaotic inflation. In particular, we discuss the evolution of inhomogeneous solutions in the neighborhood of the homogeneous isotropic background solution and their relation to the observable primordial fluctuation spectrum. If the propagators for the graviton and scalar field remain regular, our observed inhomogeneous Universe can be extrapolated back to the infinite past in physical time. In this case there is no physical big-bang singularity -- the latter reflects only a singular choice of ``field coordinates". Independently of the issue of singularity the primordial flat frame offers a new view on the physical properties of the inflationary universe, which can be characterized as a very slowly evolving almost empty vacuum state with approximate scale symmetry., additional discussion of inhomogeneous cosmological solutions and big bang singularity , 31 pages

Swampland Conjectures have attracted quite some interest in the Cosmological Community. They have been shown to have wide ranging implications , like Constraints on Inflationary Models, Primordial Black Holes etc. to name a few. A particularly revealing insight on dark energy also shows that one can have the dark energy equation of state for a quintessence scenario to be signficantly different than -1 after one takes into account the refined dS conjecture. Another interesting issue with the swampland conjectures is that they have been shown to be incompatible with single field inflationary models in GR based cosmology. In our previous work we have, however, showed that single field inflationary models are quite compatible with swampland conjectures in their usual string theoretic form in a large class of modified cosmological scenarios. Building on that work, we now show that in modified cosmological scenarios where the early universe expansion was driven by single field inflation , one can have the dark energy equation of state to be significantly different from -1 even if we just take into account the original dS conjecture, let alone the refined form of that. We thereby show that one does not need to apply a step function approach towards inflation in order to have an observable distinction between constant and non constant dark energy models in the context of the swampland conjectures., Comment: v2, 9 pages long with added references and minor details

We review the canonical quantisation of the geometry of the spacetime in the cases of a simply and a non-simply connected manifold. In the former, we analyse the information contained in the solutions of the Wheeler-DeWitt equation and interpret them in terms of the customary boundary conditions that are typically imposed on the semiclassical wave functions. In particular, we review three different paradigms for the quantum creation of a homogeneous and isotropic universe. For the quantisation of a non-simply connected manifold the best framework is the so-called third quantisation formalism, in which the wave function of the universe is seen as a field that propagates in the space of Riemannian $3$-geometries, which turns out to be isomorphic to a (part of a) $1+5$ Minkowski spacetime. Thus, the quantisation of the wave function follows the customary formalism of a quantum field theory. A general review of the formalism is given and it is analysed the creation of the universes, their initial expansion and the appearance of matter after inflation. These features are presented in more detail in the case of a homogeneous and isotropic universe. The main conclusion in both cases is that the most natural way in which the universes should be created is in entangled universe-antiuniverse pairs., 56 pages, 26 figures

Canonical formulation of higher-order theory of gravity has been attempted over decades. Different routes lead to different phase-space structures of the Hamiltonian. Although, these Hamiltonians are canonically equivalent at the classical level, their quantum counterparts may not be same, due to nonlinearity. Earlier, it has been proved that ‘Dirac constraint analysis’ (after taking care of divergent terms) and ‘Modified Horowitz’ Formalism’ lead to identical phase-space structure of the Hamiltonian for the gravitational action with scalar curvature squared terms. For the sake of completeness, this paper expatiates the extension of the same work for a general fourth-order gravitational action. Canonical quantization and semiclassical approximation are performed to explore that such a quantum theory transits successfully to a classical de-Sitter Universe. Inflation is also studied. Inflationary parameters show excellent agreement with the recently released Planck’s data.

Within the framework of inflationary model with field-dependent kinetic term for quartic and natural potentials, we investigate generation of the primordial black holes (PBHs) and induced gravitational waves (GWs). In this setup, we consider a kinetic function as $G(\phi)=g_I(\phi)\big(1+g_{II}(\phi)\big)$ and show that in the presence of first term $g_I(\phi)$ both quartic and natural potentials, in contrast to the standard model of inflation, can be consistent, with the 68\% CL of Planck observations. Besides, the second term $g_{II}(\phi)$ can cause a significant enhancement in the primordial curvature perturbations at the small scales which results the PBHs formation. For the both potentials, we obtain an enhancement in the scalar power spectrum at the scales $k\sim10^{12}~\rm Mpc^{-1}$, $10^{8}~\rm Mpc^{-1}$, and $10^{5}~\rm Mpc^{-1}$, which causes PBHs production in mass scales around $10^{-13}M_{\odot}$, $10^{-5}M_{\odot}$, and $10 M_{\odot}$, respectively. Observational constraints confirm that PBHs with a mass scale of $10^{-13}M_{\odot}$ can constitute the total of dark matter in the universe. Furthermore, we estimate the energy density parameter of induced GWs which can be examined by the observation. Also we conclude that it can be parametrized as a power-law function $\Omega_{\rm GW}\sim (f/f_c)^n$, where the power index equals $n=3-2/\ln(f_c/f)$ in the infrared limit $f\ll f_{c}$., Comment: 25 pages, 7 figures, 5 tables

We propose an experiment that the entanglement between two macroscopic mirrors suspended at the end of an equal-arm interferometer is destroyed by the noise of gravitons through bremsstrahlung. By calculating the correlation function of the noise, we obtain the decoherence time from the decoherence functional. We estimate that the decoherence time induced by the noise of gravitons in squeezed states stemming from inflation is approximately 20 seconds for 40 km long arms and 40 kg mirrors. Our analysis shows that observation of the decoherence time of quantum entanglement has the potential to detect gravitons indirectly. This indirect detection of gravitons would give strong evidence of quantum gravity., Comment: 5 pages, 2 figures

In light of the most recent cosmological observations, we provide new updated constraints on the slow-roll inflation in different extended scenarios beyond the $\Lambda\rm{CDM}$ cosmological model. Along with the usual six parameters, we simultaneously vary different combinations of additional parameters, including the running of the scalar spectral index $\alpha_s$, its running of running $\beta_s$, the tensor amplitude $r$ and the spatial curvature $\Omega_k$. From the Planck 2018 data, we find no evidence for a scalar running or a running of running, while analyzing the Atacama Cosmology Telescope data combined with WMAP 9-years observations data we find a preference for non-zero $\alpha_s$ and $\beta_s$ at the level of 2.9$\sigma$ and 2.7$\sigma$, respectively. Anyway, this preference is reduced when the tensor amplitude can vary in the model or $\beta_s$ is fixed to zero. The upper bound on $r$ is only slightly affected by the additional parameters while the differences in the datasets can remarkably change the compatibility among the different inflationary models, sometimes leading to discordant conclusions., Comment: 20 pages, 6 figures

We analyze field fluctuations during an ultra slow-roll phase in the stochastic picture of inflation and the resulting non-Gaussian curvature perturbation, fully including the gravitational backreaction of the field's velocity. By working to leading order in a gradient expansion, we first demonstrate that consistency with the momentum constraint of general relativity prevents the field velocity from having a stochastic source, reflecting the existence of a single scalar dynamical degree of freedom on long wavelengths. We then focus on a completely level potential surface, $V={V}_{0}$, extending from a specified exit point ${\ensuremath{\phi}}_{\mathrm{e}}$, where slow roll resumes or inflation ends, to $\ensuremath{\phi}\ensuremath{\rightarrow}+\ensuremath{\infty}$. We compute the probability distribution in the number of $e$-folds $\mathcal{N}$ required to reach ${\ensuremath{\phi}}_{\mathrm{e}}$, which allows for the computation of the curvature perturbation. We find that, if the field's initial velocity is high enough, all points eventually exit through ${\ensuremath{\phi}}_{\mathrm{e}}$ and a finite curvature perturbation is generated. On the contrary, if the initial velocity is low, some points enter an eternally inflating regime despite the existence of ${\ensuremath{\phi}}_{\mathrm{e}}$. In that case, the probability distribution for $\mathcal{N}$, although normalizable, does not possess finite moments, leading to a divergent curvature perturbation.

In this work, we investigate especial slow-roll regime inflation with a Gauss-Bonnet term inspired by string theory with an arbitrary potential and an arbitrary nonminimal coupling to the Gauss-Bonnet term. We have proposed a single field model which the coupling function \xi (\phi ) to the Gauss-Bonnet scalar satisfies \xi (\phi )\sim \frac{1}{V(\phi )}. There is a key point in these proposed functions. We have limited ourselves to decimal powers in these functions which give us this chance to have two different free parameters as (n, m). (The two different parameters in the potential and coupling functions.) The cosmological observable values (n_{s}, r) from this model that we have proposed, unbelievably coincide with the n_{s}-r plane favored by the Planck 2018 data.

We find that with the big bang, inflation and expansion of the universe, the quantum gravitation, gravitation and gauge field force have been separated from the high-dimensional supergravity successively, and the big rip-rebound cluster with the network distribution of quantum chaos emerges between the universe and particles, thus forming the super synergy. Under the big unified framework of quantum gravitation and quantum repulsion, the quantum repulsive field equation to the quantum gravitational field equation is set, and the quantum hedge-unified field equation describing the interaction of quantum gravitational field and quantum repulsive field is established; on this basis, the quantum repulsive universe equation to the quantum gravitational universe equation is established, thus a set of expansive universe equation of quantum hedge-unified field theory is given. Between particle physics and cosmology, the cosmic quantum evolution mode is discussed, the phys-sphere distributing configuration and the interaction situation variables, organizes the concepts, variables and models of these three levels are put forth, and establish a paradigm. In this paradigm, the general Langevan equation and the general Fokker–Planck equation are established. A series of trend parameters are introduced to establish the dynamics of quantum gravitational mode and its master equation, and then to establish the operator distribution function and its motion equation of the action mode. For the Tachyon of upheaval in the super-inflating, the quantum theory of the early photons in upheaval is set up, and the analysis on the particles of the ultrahigh energy cosmic ray from the γ-ray burst is made.

It is accepted in the present cosmology model that the scalar field, which is responsible for the inflation stage in the early universe, transforms completely into matter, and the accelerated universe expansion is presently governed by dark energy (DE), whose origin is not connected with the inflationary scalar field. We suppose here that dark matter (DM) has a common origin with a small variable component of dark energy (DEV). We suggest that DE may presently have two components, one of which is the Einstein constant Λ, and another, smaller component DEV (ΛV) comes from the remnants of the scalar field responsible for inflation, which gave birth to the origin of presently existing matter. In this note we consider only the stages of the universe expansion after recombination, z≃1100, when DM was the most abundant component of the matter, therefore we suggest for simplicity that a connection exists between DM and DEV so that the ratio of their densities remains constant over all the stages after recombination, ρDM=αρDEV, with a constant α. One of the problems revealed recently in cosmology is a so-called Hubble tension (HT), which is the difference between values of the present Hubble constant, measured by observation of the universe at redshift z≲1, and by observations of a distant universe with CMB fluctuations originated at z∼1100. In this paper we suggest that this discrepancy may be explained by deviation of the cosmological expansion from a standard Lambda-CDM model of a flat universe, due to the action of an additional variable component DEV. Taking into account the influence of DEV on the universe’s expansion, we find the value of α that could remove the HT problem. In order to maintain the almost constant DEV/DM energy density ratio during the time interval at z<1100, we suggest the existence of a wide mass DM particle distribution.

For the collided region of two gravitationally bound structures A and B, geodesic equation is derived using calculus of variations. With the help of geodesic equation derived for the collided region of A and B, a method to calculate any possible curvature of universe beyond observable flat universe is detailed. This relativistic method is used to describe a generic idea on the evolution of gravitationally bound structures and its effect on the evolution of universe. Using this idea, distribution of matter and antimatter in the universe, observed accelerating expansion of universe, cosmic inflation, and large-scale structure of present universe are explained.

We derive the quantum energy-momentum tensor and the corresponding quantum equation of state for gauge field theory using the effective Lagrangian approach. The energy-momentum tensor has a term proportional to the space-time metric and provides a finite non-diverging contribution to the effective cosmological term. This allows to investigate the influence of the gauge field theory vacuum polarisation on the evolution of Friedmann cosmology, inflation and primordial gravitational waves. The Type I-IV solutions of the Friedmann equations induced by the gauge field theory vacuum polarisation provide an alternative inflationary mechanism and a possibility for late-time acceleration. The Type II solution of the Friedmann equations generates the initial exponential expansion of the universe of finite duration and the Type IV solution demonstrates late-time acceleration. The solutions fulfil the necessary conditions for the amplification of primordial gravitational waves., Comment: 36 pages and 9 figures, references added, minor corrections

In this paper, by fully exploiting nonlinear structure of the cross term in the chemotaxis system and using microlocal analysis, we prove that this system is ill-posed for the critical case B ˙ 2 d , 1 − 3 2 × ( B ˙ 2 d , 1 − 1 2 ) d in the sense of “norm inflation”, which is an unsolved problem in [21] . This result improves the ill-posedness theories of this system in critical Besov spaces framework.

This work mainly focuses on the free swelling and inflation mechanics of a hyperelastic homogeneous and isotropic gas-filled toroidal gel balloon of an initially circular cross-section. Two compressible hyperelastic material models, namely neo-Hookean and Gent, are considered with Flory–Huggins mixing energy. Mechanics of free swelling configurations are studied using equilibrium equations obtained for incompressible and compressible axisymmetric inflation. The two-point boundary value problem of the balloon was solved using the Nelder–Meads search technique by constructing an optimization problem. Non-uniform solvent concentration is observed in the meridional direction for the equilibrium swelling and inflation. For the neo-Hookean material, the instant/delayed burst phenomenon is observed for almost all the geometric and material parametric ranges due to the softening type nonlinearity. On the other hand, for the Gent material model, instant/delayed short burst phenomenon is observed for a specific range of dimensionless material constants. The inflation pressure range for the burst phenomenon and equilibrium swelling is identified for particular material parametric ranges. The critical pressure for the delayed short burst is roughly estimated and found to be highly dependent on the nonlinear nature of the swollen toroidal gel balloon inflation pressure-stretch curve. Also, deswelling is observed at the larger inflation stretch values of the gel.

The study of inflation through different prospects is being done for specific model of scalar f ( T ) gravity in two phases such as attractor ( n s ( N ) − 1 ∝ N − 1 ) and slow roll parameterizations. In the presence of these ingredients, we evaluate all inflationary parameters such as scalar spectral index, tensor to scalar ratio r and running of scalar spectral index and local non Gaussianity parameter. We also develop the inflationary planes n s − N , r − N , d n s d ln κ − N , d n s d ln κ − n s and f N L − n s . These planes show the viability of our outcomes with Planck data 2018.