We address the problem of determining inflationary characteristics in a model independent way. We start from a recently proposed equation which allows to accurately calculate the value of the inflaton at horizon crossing $ϕ_k$. We then use an equivalent form of this equation to write a formula that relates the number of e-folds from horizon crossing to the pivot scale $N_{ke}+N_{ep}$ with the tensor-to-scalar index $r$, hence a general bound for $N_{ke}+N_{ep}$ follows. $N_{ke}$ is the number of e-folds from the scale factor $a_k$ during inflation to the end of inflation at $a_e$ and $N_{ep}$ is the number of e-folds from $a_e$ to the pivot scale factor $a_p$. In particular, at present $r < 0.063$ implies $N_{ke}+N_{ep}< 112.5$ e-folds at $k=k_p$ and 128.1 e-folds at the present scale with wavenumber mode $k_0$. We also give a lower bound to the size of the universe during the inflationary epoch that gave rise to the current observable universe. We also discussed the problem of degeneracy of inflationary models and argue that this degeneration can only be resolved by studying model predictions from the reheating epoch.
We often find in the literature solutions to the Friedmann and fluid equations for simple cosmological models during the matter, radiation or cosmological constant dominated epochs. However no solutions appear for the inflationary era dominated by the potential energy of a scalar field due, perhaps, to the fact that we do not have as yet a strongly favored model of inflation; there are, of course, very well motivated models which fit the data. The purpose of this article is to study with some detail the evolution of the Universe during inflation in the slow-roll approximation. Taking the Staro…
We present a nonlinear study of the inflationary epoch based on numerical lattice simulations. Lattice simulations are a well-known tool in primordial cosmology, and they have been extensively used to study the reheating epoch after inflation. We generalize this known machinery to the inflationary epoch. Being this the first simulation of the inflationary epoch much before the end of inflation, the first part of the thesis focuses on the minimal single-field model of inflation. We discuss the conceptual and technical ingredients needed to simulate inflation on a lattice. The simulation is used…
We present a simple formula that allows to calculate the value of the inflaton field, denoted by $ϕ$, at the scale with wavenumber mode $k$. In the extreme case of instantaneous reheating $ϕ_k$ is calculated exactly and all inflationary observables and quantities of interest follow. This formula, together with the fact that the scale factor $a_p$ at the pivot scale wavenumber $k_p=0.05/Mpc$ lies in the radiation era, allows the development of a diagrammatic approach to study the evolution of the universe. This scheme is complementary to the usual analytical method and some interesting results,…
We analyze the effects of the holographic dark energy model in a single field slow-roll inflation, taking into account both the holographic and the dark radiation components. In particular, we obtain the background evolution and compute the scalar and tensor power spectra. For the scalar sector we show that the power spectrum of the curvature perturbation encompasses the standard single field result and a correction proportional to $Ω_{\rm hde}/ε$, where $Ω_{\rm hde}$ is the fractional density of the holographic component and $ε$ is the first slow-roll parameter. This correction might be of or…
When large overdensities gravitationally collapse in the early universe, they lead to primordial black holes (PBH). Depending on the exact model of inflation leading to necessary large perturbations at scales much smaller than scales probed at the Cosmic Microwave Background (CMB) surveys, PBHs of masses $\lesssim$$10^3 M_{\odot}$ can be formed sometime between the end of inflation and nucleosynthesis. However, the lack of a direct probe for the exact expansion history of the universe in this duration introduces uncertainties in the PBH formation process. The presence of alternate cosmological…
The discovery of many novel realizations of the inflationary universe paradigm has led to a degeneracy problem: many different inflationary Lagrangians generate the same perturbation spectra. Resolving this problem requires the future discovery of additional observables, beyond the scalar adiabatic and tensor two-point functions on CMB scales. One important source of degeneracy arises in models where the density perturbation is generated by a non-inflationary degree of freedom, for example, through curvatons or modulated reheating. We consider the curvaton scenario as representative of this cl…
From the assumption that the slow roll parameter $ε$ has a Lorentzian form as a function of the e-folds number $N$, a successful model of a quintessential inflation is obtained. The form corresponds to the vacuum energy both in the inflationary and in the dark energy epochs. The form satisfies the condition to climb from small values of $ε$ to $1$ at the end of the inflationary epoch. At the late universe $ε$ becomes small again and this leads to the Dark Energy epoch. The observables that the models predicts fits with the latest Planck data: $r \sim 10^{-3}, n_s \approx 0.965$. Naturally a la…
We discuss whether an unaccounted contribution to the Cosmic Microwave Background polarization $B$-mode by primordial magnetic fields (PMFs) can bias future constraints on inflationary gravitational waves. As a case-study, we consider a scale-invariant PMF spectrum with amplitude of $\approx{1}\,{\mathrm{nG}}$ on $1\,\mathrm{Mpc}$ scales, compatible with current cosmological bounds. We find a degeneracy in the $B$-mode spectra between PMFs and inflationary gravitational waves. If PMFs of this amplitude are not accounted for, future CMB experiments could claim a false detection of a tensor-to-s…
Pre-inflationary dynamics is known to have left observable imprints via the varied dynamics of the inflaton and the graviton fields during those epochs. It is highlighted here that other particle degrees of freedom, too, are capable of leaving their imprints on primordial observables if they transfer their entropies upon annihilation after becoming non-relativistic during a pre-inflationary epoch. Such annihilations of other particles would result in lowering of the tensor-to-scalar ratio at the pivot scale (and at length scales larger to that) which would help bring those potentials back in a…
The trace of the stress-energy tensor of the cosmological fluid, proportional to the Ricci scalar curvature in general relativity, is determined on cosmic scales for times ranging from the inflationary epoch to the present day in the expanding Universe. The post-inflationary epoch and the thermal history of the relativistic fluid, in particular the QCD transition from asymptotic freedom to confinement and the electroweak phase transition, leave significant imprints on the scalar curvature. These imprints can be of either sign and are orders of magnitude larger than the values that would be obt…
We study the polynomial chaotic inflation model with a single scalar field in a double well quartic potential which has recently been shown to be consistent with Planck data. In particular, we study the effects of lifting the degeneracy between the two vacua on the inflationary observables, i.e. spectral index n_s and tensor-to-scalar perturbation ratio r_T. We find that removing the degeneracy allows the model to satisfy the upper limit constraints on r_T from Planck data, provided the field starts near the local maximum. We also calculate the scalar power spectrum and non-Gaussianity paramet…
Using the latest observational data we obtain a lower bound on the initial value of the quintessence field in thawing quintessence models of dark energy. For potentials of the form V(ϕ) ϕ^{\pm2} we find that the initial value |ϕ_i|>7x10^{18}\gev. We then relate ϕ_i to the duration of inflation by assuming that the initial value of the quintessence field is determined by quantum fluctuations of the quintessence field during inflation. From the lower bound on $ϕ_i$ we obtain a lower bound on the number of e-foldings of inflation, namely, N>2x10^{11}. We obtain similar bounds for other power law …
If the inflaton and the quintessence fields are identified, the background geometry evolves through a stiff epoch undershooting the expansion rate of a radiation-dominated plasma. For some classes of inflationary potentials this scenario is at odds with the current observational evidence since the corresponding tensor-to-scalar ratio is too large. Quintessential inflation is analyzed when the gravitational action is supplemented by a contribution quadratic in the Einstein-Hilbert term. In the Palatini formulation the addition such a term does not affect the scalar modes during the inflationary…
We investigate cosmological scenarios in the theory of gravity with the scalar field possessing a non-minimal kinetic coupling to the curvature. It is shown that the kinetic coupling provides an essentially new inflationary mechanism. Namely, at early cosmological times the domination of coupling terms in the field equations guarantees the quasi-De Sitter behavior of the scale factor: $a(t)\propto e^{H_κ t}$ with $H_κ=1/\sqrt{9κ}$, where $κ\simeq 10^{-74}$ sec$^2$ is the coupling parameter. The primary inflationary epoch driven by non-minimal kinetic coupling comes to the end at $t_f \simeq 10…
$R^2$-corrected dark energy (DE) models in $F(R)$ gravity have been widely investigated in recent years, which not only removes the weak singularity potentially present in DE models but also provide us with a unified picture of the cosmic history, including the inflationary and DE epochs. Towards the unified interpretation of dynamical DE all over the cosmic history in the class of $R^2$-corrected DE models, we explore the universal features of the scalaron dynamics in the radiation-dominated epoch, along with the chameleon mechanism, by keeping our eyes on the inflationary and DE epochs. We s…
Inflation in the early Universe is one of the most promising probes of gravity in the high-energy regime. However, observable scales give access to a limited window in the inflationary dynamics. In this essay, we argue that quantum corrections to the classical dynamics of cosmological fields allow us to probe much earlier epochs of the inflationary phase and extend this window by many orders of magnitude. We point out that both the statistics of cosmological fluctuations at observable scales, and the field displacements acquired by spectator fields that play an important role in many post-infl…
From the assumption that the slow roll parameter $ε$ has a Lorentzian form as a function of the e-folds number $N$, a successful model of a quintessential inflation is obtained, as succinctly studied in \cite{Benisty:2020xqm}. The form corresponds to the vacuum energy both in the inflationary and in the dark energy epochs and satisfies the condition to climb from small values of $ε$ to $1$ at the end of the inflationary epoch. We find the corresponding scalar Quintessential Inflationary potential with two flat regions. Moreover, a reheating mechanism is suggested with numerical estimation for …
We analyse the epoch of reheating after an inflationary phase in the Randal Sundrum(RS) Type-$\rm II$ braneworld, where we did not consider any particular model of inflation, but rather reconstructed the inflationary potential solving the flow equations using Monte Carlo (MC) approach. It is shown numerically that a potential conceived through the MC reconstruction technique can be represented by an effective potential as a function of the number of e-foldings($N$). Then, the epoch of reheating is studied for this reconstructed potential. The relation between the reheating temperature ($T_{\rm…
Creation of an inflationary epoch from an Emergent Universe through quantum tunneling
Ben Gurion University of the Negev（内盖夫本-古里安大学）；Frankfurt Institute for Advanced Studies（法兰克福高等研究所）；Bahamas Advanced Studies Institute and Conferences（巴哈马高级研究与会议研究所）
We investigate the problem of perturbative reheating and its effects on the evolution of the curvature perturbations in tachyonic inflationary models. We derive the equations governing the evolution of the scalar perturbations for a system consisting of a tachyon and a perfect fluid. Assuming the perfect fluid to be radiation, we solve the coupled equations for the system numerically and study the evolution of the perturbations from the sub-Hubble to the super-Hubble scales. In particular, we analyze the effects of the transition from tachyon driven inflation to the radiation dominated epoch o…
We derive a lower bound on the field excursion for the tachyon inflation, which is determined by the amplitude of the scalar perturbation and the number of $e$-folds before the end of inflation. Using the relation between the observables like $n_s$ and $r$ with the slow-roll parameters, we reconstruct three classes of tachyon potentials. The model parameters are determined from the observations before the potentials are reconstructed, and the observations prefer the concave potential. We also discuss the constraints from the reheating phase preceding the radiation domination for the three clas…
The post-inflationary evolution of inflation-produced magnetic fields, conventional or not, can change dramatically when two fundamental issues are accounted for. The first is causality, which demands that local physical processes can never affect superhorizon perturbations. The second is the nature of the transition from inflation to reheating and then to the radiation era, which determine the initial conditions at the start of these epochs. Causality implies that inflationary magnetic fields dot not freeze into the matter until they have re-entered the causal horizon. The nature of the cosmo…
Recent population studies have searched for a subpopulation of primordial black holes (PBHs) in the gravitational-wave (GW) events so far detected by LIGO/Virgo/KAGRA (LVK), in most cases adopting a phenomenological PBH mass distribution. When deriving such population from first principles in the standard scenario, however, the equation of state of the Universe at the time of PBH formation may strongly affect the PBH abundance and mass distribution, which ultimately depend on the power spectrum of cosmological perturbations. Here we improve on previous population studies on several aspects: (i…
We explore possible constraints on the inflationary equation state: p=wρ. While w must be close to -1 for those modes that contribute to the observed power spectrum, for those modes currently out of experimental reach, the constraints on w are much weaker, with only w<-1/3 as an a priori requirement. We find, however, that limits on the reheat temperature and the inflationary energy scale constrain w further, though there is still ample parameter space for a vastly different (accelerating) equation of state between the end of quasi-de Sitter inflation and the beginning of the radiation-dominat…
We study to what extent the spectral index $n_s$ and the tensor-to-scalar ratio $r$ determine the field excursion $Δϕ$ during inflation. We analyse the possible degeneracy of $Δϕ$ by comparing three broad classes of inflationary models, with different dependence on the number of e-foldings $N$, to benchmark models of chaotic inflation with monomial potentials. The classes discussed cover a large set of inflationary single field models. We find that the field range is not uniquely determined for any value of $(n_s, r)$; one can have the same predictions as chaotic inflation and a very different…
For a robust interpretation of upcoming observations from Planck and LHC experiments it is imperative to understand how the inflationary dynamics of a non-minimally coupled Higgs scalar field may affect the degeneracy of the inflationary observables. We constrain the inflationary observables and the Higgs boson mass during observable inflation by fitting the the Higgs inflationary potential directly to WMAP5+BAO+SN data. We obtain a Higgs mass a value of 143.73+14.97/-6.31 GeV at 95% CL for the central value of top quark mass. We also show that the inflation driven by a non-minimally coupled s…
Generation of magnetic field during inflation can explain its presence over a wide range of scales in the Universe. In Ref.\cite{sharma2017}, we proposed a model to generate these fields during inflation. These fields have nonzero anisotropic stress which lead to the generation of a stochastic background of gravitational waves (GW) in the early universe. Here we show that for a scenario of magnetogenesis where reheating takes place around QCD epoch, this stochastic GW background lies in the $95\%$ confidence region of the GW signal probed by NANOGrav collaboration. This is the case when the ge…
The possibility of having an inflationary epoch within a noncommutative geometry approach to unifying gravity and the standard model is demonstrated. This inflationary phase occurs without the need to introduce "ad hoc" additional fields or potentials, rather it is a consequence of a nonminimal coupling between the geometry and the Higgs field.
Motivated by the fact that the pre-inflationary era may evolve in an exotic way, in this work we formalize anisotropic evolution in the context of modified gravity, focusing on pre-inflationary and near the vicinity of the inflationary epochs. We specialize on specific metrics like Bianchi and Taub and we formalize the inflationary theory in vacuum $F(R)$ gravity, in $F(R)$ gravity with an extra scalar field and in Gauss-Bonnet gravity. We discuss the qualitative effects of the anisotropies on the evolution of the Universe and also we consider several specific solutions, like the de Sitter sol…
We study $F(R)$ modified gravity models which are capable of driving the accelerating epoch of the Universe at the present time whilst not destroying the standard Big Bang and inflationary cosmology. Recent studies have shown that a weak curvature singularity with $|R|\to\infty$ can arise generically in viable $F(R)$ models of present dark energy (DE) signaling an internal incompleteness of these models. In this work we study how this problem is cured by adding a quadratic correction with a sufficiently small coefficient to the $F(R)$ function at large curvatures. At the same time, this correc…
We make a more general determination of the inflationary observables in the standard 4-D and 5-D single-field inflationary scenarios, by the exact reconstruction of the dynamics of the inflation potential during the observable inflation with minimal number of assumptions: the computation does not assume the slow-roll approximation and is valid in all regimes if the field is monotonically rolling down its potential. Making use of the {\em Hamilton-Jacobi} formalism developed for the 5-D single-field inflation model,we compute the scale dependence of the amplitudes of the scalarand tensor pertur…
While attempting to connect inflationary theories to observational physics, a potential difficulty is the degeneracy problem: a single set of observables maps to a range of different inflaton potentials. Two important classes of models affected by the degeneracy problem are canonical and non-canonical models, the latter marked by the presence of a non-standard kinetic term that generates observables beyond the scalar and tensor two-point functions on CMB scales. The degeneracy problem is manifest when these distinguishing observables go undetected. We quantify the size of the resulting degener…
Realizing the inflationary epoch driven by a pseudo-Nambu Goldstone boson (pNGB) could ensure the coveted flatness, and the sub-Planckian scales related to the dynamics of the paradigm. In this work, we have taken the most general form of such a scenario: Goldstone inflation proposed in \cite{croon}, and studied the model in Einstein-Gauss-Bonnet gravity. Natural inflation is a limiting case of this model, is also studied here. The specific form of the EGB coupling gives ample opportunity to study the rich phenomenology associated with inflation as well as the reheating epoch. Predicted values…
We conduct a model-independent analysis of temporal features during inflation in the large-scale CMB temperature power spectrum allowing for the possibility of non-negligible tensor contributions. Of 20 principal components of the inflationary history, the suppression of power at low multipoles beginning with a glitch at multipoles $\ell \sim 20-40$ implies deviations in 2-3 of them with 2-3$σ$ deviations in each, with larger values reflecting cases where tensors are allowed.If tensors are absent, the corresponding $E$-mode polarization features follow a similar pattern but are predicted to be…
Inflationary scenarios in string theory often involve a large number of light scalar fields, whose presence can enrich the post-inflationary evolution of primordial fluctuations generated during the inflationary epoch. We provide a simple example of such post-inflationary processing within an explicit string-inflationary construction, using a Kahler modulus as the inflaton within the framework of LARGE Volume Type-IIB string flux compactifications. We argue that inflationary models within this broad category often have a selection of scalars that are light enough to be cosmologically relevant,…
In this article, I have studied the cosmological and particle physics constraints on a generic class of large field ($|Δϕ|>M_{p}$) and small field ($|Δϕ<M_{p}$) models of brane inflationary magnetic field from: (1) tensor-to-scalar ratio ($r$), (2) reheating, (3) leptogenesis and (4) baryogenesis in case of Randall-Sundrum single braneworld gravity (RSII) framework. I also establish a direct connection between the magnetic field at the present epoch ($B_{0}$) and primordial gravity waves ($r$), which give a precise estimate of non-vanishing CP asymmetry ($ε_{CP}$) in leptogenesis and baryon as…
We study how direct detection of the inflationary gravitational wave background constrains inflationary parameters and complements CMB polarization measurements. The error ellipsoids calculated using the Fisher information matrix approach with Planck and the direct detection experiment, BBO (Big Bang Observer), show different directions of parameter degeneracy, and the degeneracy is broken when they are combined. For a slow-roll parameterization, we show that BBO could significantly improve the constraints on the tensor-to-scalar ratio compared with Planck alone. We also look at a quadratic an…
Inflationary models involving more than one scalar field naturally produce isocurvature perturbations. However, while these are fairly well studied, less is known about their evolution through the reheating epoch, when the inflationary fields decay into the standard constituents of the present universe. In this paper, by modelling reheating perturbatively, we calculate the power spectrum of the non-adiabatic pressure perturbation in three different inflationary models. We show that the isocurvature can grow large initially, but decays faster than the pressure perturbations. When reheating ends…
In models of inflation obtained from string compactification, moduli vacuum misalignment leads to an epoch in the post-inflationary history of the universe when the energy density is dominated by cold moduli particles. This effect leads to a modification in the number of $e$-foldings ($N_{\rm pivot}$) between horizon exit of the CMB modes and the end of inflation. Taking Kähler moduli inflation as a prototype, the shift in $e$-foldings turns out to be a function of the model parameters which also determines the inflationary observables. We analyse this scenario numerically using publicly avail…
I consider the question of possible observability of the total number of e-folds accumulated during the epoch of inflation. The total number of observable e-folds has been previously constrained by the de Sitter entropy after inflation, assuming that the null energy condition (NEC) holds. The NEC is violated by upward fluctuations of the local Hubble rate, which occur with high probability in the fluctuation-dominated regime of inflation. These fluctuations lead at late times to the formation of black holes and thus limit the observability of inflationary evolution. I compute the maximum numbe…
[Abridged] As is well known, in order to generate magnetic fields of observed amplitudes during inflation, the conformal invariance of the electromagnetic field has to be broken by coupling it either to the inflaton or to the scalar curvature. Couplings to scalar curvature pose certain challenges even in slow roll inflation and it seems desirable to consider couplings to the inflaton. It can be shown that, in slow roll inflation, to generate nearly scale invariant magnetic fields of adequate strengths, the non-conformal coupling to the inflaton has to be chosen specifically depending on the in…
If, after primordial inflation, the universe undergoes a relatively long reheating period, it could present a phase of matter domination supported by the oscillating inflaton field. During this epoch, small perturbations from the inflaton that reenter the cosmological horizon could virialize to form \textit{inflaton} structures. If the primordial overdensities are large enough, their associated inflaton structures could collapse to form primordial black holes (PBHs) [L.E.Padilla, J.C.Hidalgo and K.A.Malik, Phys.Rev.D, vol.106, p.023519, Jul 2022; hereinafter P1]. For this to happen at a consid…
The recently proposed Trans-Planckian Censorship Conjecture (TCC) can be used to constrain the energy scale of inflation. The conclusions however depend on the assumptions about post-inflationary history of the Universe. E.g. in the standard case of a thermal post-inflationary history in which the Universe stays radiation dominated at all times from the end of inflation to the epoch of radiation matter equality, TCC has been used to argue that the Hubble parameter during inflation, $H_{\inf}$, is below ${\cal O}(0.1) ~{\rm GeV}$. Cosmological scenarios with a non-thermal post-inflationary hist…
Using a semiclassical approach to Gravitoelectromagnetic Inflation (GEMI), we study the origin and evolution of seminal inflaton and electromagnetic fields in the early inflationary universe from a 5D vacuum state. We use simultaneously the Lorentz and Feynman gauges. Our formalism is naturally not conformal invariant on the effective 4D de Sitter metric, which make possible the super adiabatic amplification of electric and magnetic field modes during the early inflationary epoch of the universe on cosmological scales. This is the first time that solutions for the electric field fluctuations a…
We study the overshoot problem in the context of post-inflationary string cosmology (in particular LVS). LVS cosmology features a long kination epoch as the volume modulus rolls down the exponential slope towards the final minimum, with an energy density that scales as $m_s^4$. This roll admits attractor tracker solutions, and if these are located the overshoot problem is solved. We show that, provided a sufficiently large hierarchy exists between the inflationary scale and the weak scale, this will always occur in LVS as initial seed radiation grows into the tracker solution. The consistency …
In this paper, we embed the model of flipped GUT sneutrino inflation -in a flipped SU(5) or SO(10) set up- developed by Ellis et al. in a supergravity framework. The GUT symmetry is broken by a waterfall which could happen at early or late stage of the inflationary period. The full field dynamics is thus studied in detail and these two main inflationary configurations are exposed, whose cosmological predictions are both in agreement with recent astrophysical measurements. The model has an interesting feature where the inflaton has natural decay channels to the MSSM particles allowed by the GUT…
We analyse the self-consistency of inflation in the Standard Model, where the Higgs field has a large non-minimal coupling to gravity. We determine the domain of energies in which this model represents a valid effective field theory as a function of the background Higgs field. This domain is bounded above by the cutoff scale which is found to be higher than the relevant dynamical scales throughout the whole history of the Universe, including the inflationary epoch and reheating. We present a systematic scheme to take into account quantum loop corrections to the inflationary calculations within…
