arXiv subjects

Akhilesh Nautiyal

Publications and source records attributed to Akhilesh Nautiyal.

18 recordsLinked to original sources

arXiv2026

Power law $α$-Starobinsky inflation

In this work we consider a generalization of Starobinsky inflation obtained by combining power law ($R^β$), and $α$-Starobinsky inflation ($E$-model). The Einstein frame potential for this model is that of power law Starobinsky inflation modified by a parameter $α$ in the exponential. After computing power spectra for scalar and tensor perturbations numerically, we perform MCMC analysis to put constraints on the potential parameters $α$, $β$ and $M$, and the number of e-foldings $N_{pivot}$ during inflation, using Planck-2018, BICEP/Keck (BK18), DES and BAO observations. We find $\log_{10}α= 0.37^{+0.82}_{-0.85}$, $β= 1.969^{+0.020}_{-0.023}$, $M=\left(3.54^{+2.62}_{-1.73}\right)\times 10^{-5}$ and $N_{pivot} = 47\pm{10}$. With these mean values of the potential parameters $α$ and $β$, and varying $N_{pivot}$ between $40$ to $55$, we also find that the $r-n_s$ predictions of our model lie well within the $1σ$ bounds of joint constraints from combined analysis of ACT, Planck-2018, BICEP and BAO observations. We compute the Bayesian evidences for our proposed model, power law Starobinsky inflation, $α$-Starobinsky inflation and Starobinsky inflation. Considering the Starobinsky model as the base model, we calculate the Bayes factor and find that our proposed model is mildly favored by the CMB and LSS observations.

astro-ph.CO↗

arXiv2025

Observational constraints on $α$-Starobinsky inflation

In this work we revisit $α$-Starobinsky inflation, also know as $E$-model, in the light of current CMB and LSS observations. The inflaton potential in the Einstein frame for this model contains a parameter $α$ in the exponential, which alters the predictions for the scalar and tensor power spectra of Starobinsky inflation. We obtain these power spectra numerically without using slow-roll approximation and perform MCMC analysis to put constraints on parameters $M$ and $α$ from Planck-2018, BICEP/Keck (BK18) and other LSS observations. We consider general reheating scenario by varying the number of e-foldings during inflation, $N_{pivot}$, along with the other parameters. We find $\log_{10}α= 0.0^{+1.6}_{-5.6}$, $\log_{10}M= -4.91^{+0.69}_{-2.7}$ and $N_{pivot} = 53.2^{+3.9}_{-5}$ with $95\%$ C. L.. This implies that the present CMB and LSS observations are insufficient to constrain the parameter $α$. We also find that there is no correlation between $N_{pivot}$ and $α$.

astro-ph.CO↗

arXiv2025

Exploring generalized Starobinsky Model of Inflation: Observational Constraints

We examine the power-law Starobinsky model, a generalized version of the Starobinsky inflation model, characterized by a power-law correction to Einstein gravity. Employing the $f(R)$ formalism, the scalar and tensor power spectra were numerically computed as functions of the dimensionless parameters $M$ and $β$. A Markov Chain Monte Carlo (MCMC) analysis was conducted using Planck-2018, BICEP3 and BAO observational data, yielding precise constraints on $β= 1.987^{+0.013}_{-0.016},\, 95\%\, C.\, L.$. and $ \log_{10}M = -4.72^{+0.21}_{-0.20}$. The derived scalar spectral index $n_s=0.9676^{+0.0069}_{-0.0068}$ and tensor-to-scalar ratio $r=0.0074^{+0.0061}_{-0.0044}$ lie within the bounds set by Planck observations. We analyse a general reheating scenario while keeping the number of e-folds during inflation, $N_{pivot}$, fixed. The analysis confirms that deviations from the Starobinsky $R^2$ model are observationaly viable, with implications for high-energy physics and supergravity-based inflationary models.

astro-ph.CO↗

arXiv2024

Non-canonical Higgs inflation

The large value of non-minimal coupling constant $ξ$ required to satisfy CMB observations in Higgs inflation violates unitarity. In this work we study Higgs-inflation with non-canonical kinetic term of DBI form to find whether $ξ$ can be reduced. To study the inflationary dynamics, we transform the action to the Einstein frame, in which the Higgs is minimally coupled to gravity with a non-canonical kinetic term and modified potential. We choose the Higgs self coupling constant $λ=0.14$ for our analysis. We find that the value of $ξ$ can be reduced from $10^{3}-10^{4}$ to $\mathcal{O}(10)$ to satisfy Planck constraints on amplitude of scalar power spectrum. However, this model produces a larger tensor-to-scalar ratio $r$, in comparison to the Higgs inflation with canonical kinetic term. We also find that, to satisfy joint constraints on scalar spectral index $n_s$ and tensor-to-scalar ratio $r$ from Planck-2018 and bounds on $r$ from Planck and BICEP3, the value of $ξ$ should be of the order of $10^4$. Thus, the issue of unitarity violation remains even after considering Higgs inflation with non-canonical kinetic term

astro-ph.CO↗

arXiv2023

Observational constraints on power law Starobinsky inflation

In this work we revisit power law, $\frac{1}{M^2}R^β$, inflation to find the deviations from $R^2$ inflation allowed by current CMB and LSS observations. We compute the power spectra for scalar and tensor perturbations numerically and perform MCMC analysis to put constraints on parameters $M$ and $β$ from Planck-2018, BICEP3 and other LSS observations. We consider general reheating scenario and also vary the number of e-foldings during inflation, $N_{pivot}$, along with the other parameters. We find $β= 1.966^{+0.035}_{-0.042}$, $M= \left(3.31^{+5}_{-2}\right)\times 10^{-5}$ and $N_{pivot} = 41^{+10}_{-10}$ with $95\%\, C.\, L.$. This indicates that the current observations allow deviation from Starobinsky inflation. The scalar spectral index, $n_s$, and tensor-to-scalar ratio, $r$, derived from these parameters, are consistent with the Planck and BICEP3 observations.

astro-ph.CO↗

arXiv2021

Reheating constraints on K-inflation

In this work we revisit constraints on K-inflation with DBI kinetic term and power-law kinetic term from reheating. For DBI kinetic term we choose monomial potentials, $V\propto ϕ^n$ with $n=2/3\,,1\,,\,2$ and $4$, and natural inflaton potential, and for power-law kinetic term we choose quadratic, quartic and exponential potentials. The phase of reheating can be parameterized in terms of reheating temperature $T_{re}$, number of e-folds during reheating $N_{re}$ and effective equation of state during reheating $w_{re}$. These parameters can be related to the spectral index $n_s$ and other inflationary parameters depending on the choice of inflaton kinetic term and potential. By demanding that $w_{re}$ should have a finite range and $T_{re}$ should be above electroweak scale, one can obtain the bounds on $n_s$ that can provide bounds on tensor-to-scalar ratio $r$. We find, for K-inflation with DBI kinetic term and quadratic and quartic potentials, that the upper bound on $r$ for physically plausible value of $0\le w_{re} \le 0.25$ is slightly larger than the Planck-2018 and BICEP2/Keck array bound, and for $n=2/3$ and $1$, the reheating equation of state should be less than $0$ to satisfy Planck-2018 joint constraints on $n_s$ and $r$. However, natural inflation with DBI kinetic term is compatible with Planck-2018 bounds on $r$ and joint constraints on $n_s$ and $r$ for physically plausible range $0 \le w_{re}\le 0.25$. The quadratic and quartic potential with power-law kinetic term are also compatible with Planck-2018 joint constraints on $n_s$ and $r$ for $0\le w_{re} \le 1$. However, for exponential potential with power-law kinetic term, the equation of state during reheating $w_{re}$ should be greater than $1$ for $r-n_s$ predictions to lie within $68\%$C.L. of joint constraints on $n_s$ and $r$ from Planck-2018 observations.

astro-ph.CO↗

arXiv2021

Constraints on electromagnetic form factors of sub-GeV dark matter from the Cosmic Microwave Background anisotropy

We consider dark matter which have non-zero electromagnetic form factors like electric/magnetic dipole moments and anapole moment for fermionic dark matter and Rayleigh form factor for scalar dark matter. We consider dark matter mass $m_χ> \cal{ O}({\rm MeV})$ and put constraints on their mass and electromagnetic couplings from CMB and LSS observations. Fermionic dark matter with non-zero electromagnetic form factors can annihilate to $e^+ e^-$ and scalar dark matter can annihilate to $2γ$ at the time of recombination and distort the CMB. We analyze dark matter with multipole moments with Planck and BAO observations. We find upper bounds on anapole moment $g_{A}<7.163\times 10^{3} \text{GeV}^{-2}$, electric dipole moment ${\cal D}<7.978\times 10^{-9} \text{e-cm}$, magnetic dipole moment $μ<2.959\times 10^{-7} μ_B$, and the bound on Rayleigh form factor of dark matter is $g_4/Λ_4^2<1.085\times 10^{-2}\text{GeV}^{-2}$ with $95\%$C.L.

hep-ph↗

arXiv2018

Reheating constraints on Tachyon Inflation

Tachyon inflation is one of the most attractive models of noncannonical inflation motivated by string theory. In this work we revisit the constraints on tachyon inflation with inverse $\cosh$ potential and exponential potential considering reheating, Although the phase of reheating is not well understood, it can be parameterized in terms of reheating temperature $T_{re}$, number of e-folds during reheating $N_{re}$ and effective equation of state during reheating $w_{re}$, which can be related to the parameters of the tachyon potential, spectral index $n_s$ and tensor-to-scalar ratio $r$. For various reheating scenarios there is a finite range of $w_{re}$ and the reheating temperature should be above electroweak scale. By imposing these conditions, we find that both the inverse $\cosh$ potential and exponential potential are disfavored by Planck observations. We also find that $w_{re}$ for both these potentials should be close to $1$ to satisfy Planck-2015 joint constraints on $n_s$ and $r$.

astro-ph.CO↗

arXiv2017

A New f(R) Model in the Light of Local Gravity Test and Late-time Cosmology

We propose a new model of f(R) gravity containing Arctan function in the lagrangian. We show here that this model satisfies fifth force constraint unlike a similar model in Kruglov 2013. In addition to this, we carry out the fixed point analysis as well as comment on the existence of curvature singularity in this model. The cosmological evolution for this f(R) gravity model is also analyzed in the Freidmann Robertson Walker(FRW) background. To understand observational significance of the model, cosmological parameters are obtained numerically and compared with those of Lambda cold dark matter (ΛCDM) model. We also scrutinize the model with supernova data. We apply Om diagnostic given by Sahni et al. 2008 to the model. Using this diagnostic, we detect the distinction between cosmic evolution caused by the f(R) model and ΛCDM. We find best-fit parameter values of the model using Baryon Acoustic Oscillations data.

physics.gen-ph↗

arXiv2015

Red and blue tilted tensor spectrum from Gibbons-Hawking temperature

The scale invariant scalar and tensor perturbations, which are predicted from inflation, are eigenmodes in the conformal coordinates. The 'out' observer in the de Sitter space observes a thermal spectrum with a Gibbons-Hawking temperature $H/2π$ of these 'Bunch-Davies' particles. The tensor power spectrum observed in experiments can have an imprint of the Gibbons-Hawking thermal distribution due to the mode mixing between 'in' state conformal coordinates and the coordinate frame of the observer. We find that the the Bunch-Davies modes appear as thermal modes to the asymptotic Minkowski observer in the future and the power spectrum of the gravitational waves is blue-tilted with a spectral index $n_T \sim 1$ even in the standard slow-roll inflation. On the other hand if the coordinate frame of the observer is taken to be static coordinates, the tensor spectrum is red-tilted with $n_T\sim -1$. A likelihood analysis shows and find the best fit values of the slow-roll parameters for both cases. We find that the blue-tilted tensor gives a better fit and reconciles the PLANCK upper bound on the tensor-to-scalar ratio, $r <0.11$ with BICEP2 measurement of $r=0.2$. This supports the idea of particle production due to the mode mixing between the initial Bunch-Davies vacuum modes and the asymptotic Minkowski vacuum of the post-inflation universe.

hep-ph↗

arXiv2013

Anisotropic non-gaussianity with noncommutative spacetime

We study single field inflation in noncommutative spacetime and compute two-point and three-point correlation functions for the curvature perturbation. We find that both power spectrum and bispectrum for comoving curvature perturbation are statistically anisotropic and the bispectrum is also modified by a phase factor depending upon the noncommutative parameters. The non-linearity parameter $f_{NL}$ is small for small statistical anisotropic corrections to the bispectrum coming from the noncommutative geometry and is consistent with the recent PLANCK bounds. There is a scale dependence of $f_{NL}$ due to the noncommutative spacetime which is different from the standard single field inflation models and statistically anisotropic vector field inflation models. Deviations from statistical isotropy of CMB, observed by PLANCK can tightly constraint the effects due to noncommutative geometry on power spectrum and bispectrum.

astro-ph.CO↗

arXiv2013

Deviation From ΛCDM With Cosmic Strings Networks

In this work, we consider a network of cosmic strings to explain possible deviation from ΛCDM behaviour. We use different observational data to constrain the model and show that a small but non zero contribution from the string network is allowed by the observational data which can result in a reasonable departure from ΛCDM evolution. But by calculating the Bayesian Evidence, we show that the present data still strongly favour the concordance ΛCDM model irrespective of the choice of the prior.

astro-ph.CO↗

arXiv2012

Thawing Versus. Tracker Behaviour: Observational Evidence

Currently there is a variety of scalar field models to explain the late time acceleration of the Universe. This includes the standard canonical and non-canonical scalar field models together with recently proposed Galileon scalar field models. One can divide all these scalar field models into two broad categories, namely the thawing and the tracker class. In this work we investigate the evidence for these models with the presently available observational data using the Bayesian approach. We use the Generalized Chaplygin Gas (GCG) parametrization for dark energy equation of state (EoS) as it gives rise to both the thawing and tracking behaviours for different values of the parameters. Analysis of the observational data does not give any clear evidence for either thawing or tracking behaviour within the context of background cosmology, However, if we consider the evolution of inhomogenities and analyze the data in this context then there is a significant evidence in favour of thawing behaviour.

astro-ph.CO↗

arXiv2012

Warm natural inflation

In warm inflation models there is the requirement of generating large dissipative couplings of the inflaton with radiation, while at the same time, not de-stabilising the flatness of the inflaton potential due to radiative corrections. One way to achieve this without fine tuning unrelated couplings is by supersymmetry. In this paper we show that if the inflaton and other light fields are Pseudo-Nambu-Goldstone Bosons then the radiative corrections to the potential are suppressed and the thermal corrections are small as long as the temperature is below the symmetry breaking scale. In such models it is possible to fulfill the contrary requirements of an inflaton potential which is stable under radiative corrections and the generation of a large dissipative coupling of the inflaton field with other light fields. We construct a warm inflation model which gives the observed CMB-anisotropy amplitude and spectral index where the symmetry breaking is at the GUT scale.

hep-ph↗

arXiv2011

WMAP Constraints On K-Inflation

We study the K-Inflation models where the inflaton field has non-canonical kinetic term. In particular, we consider the Dirac-Born-Infeld (DBI) form for the kinetic energy of the inflaton field. We consider quadratic and quartic potentials as well as the potential for the natural inflation. We use a modified version of the MODECODE (proposed by Mortonson et al.) to calculate the power spectrum of the primordial perturbations generated by the inflaton field and subsequently use the WMAP7 results to constrain the models. Interestingly with DBI type kinetic term, lesser gravity waves are produced as one approaches more towards scale invariance. This is true for all the potentials considered. Unlike the canonical case, this feature, in particular, helps the quartic ($λϕ^4$) potential with DBI type kinetic term to be consistent with WMAP data.

astro-ph.CO↗

arXiv2008

Natural inflation at the GUT scale

Natural inflation driven by Pseudo-Nambu-Goldstone bosons have a problem that the nearly scale invariant spectrum of density perturbations is attained only when the symmetry breaking scale is of the order of Planck scale. We show here that if one couples the PNGB to a thermal bath as in warm inflation models, the amplitude and spectral index which agrees with the WMAP data is obtained with the symmetry breaking in the GUT scale. We give a GUT model of PNGB arising out of spontaneously broken lepton number at the GUT scale which gives rise to heavy Majorana masses for the right handed neutrinos which is needed in see-saw models. This model also generates a lepton asymmetry because of the derivative coupling of the PNGB to the lepton current. A characteristic feature of this model is the prediction of large non-gaussianity which may be observed in the forthcoming PLANCK experiment.

hep-ph↗

arXiv2007

Imprint of spatial curvature on inflation power spectrum

If the universe had a large curvature before inflation there is a deviation from the scale invariant perturbations of the inflaton at the beginning of inflation. This may have some effect on the CMB anisotropy at large angular scales. We calculate the density perturbations for both open and closed universe cases using the Bunch-Davies vacuum condition on the initial state. We use our power spectrum to calculate the temperature anisotropy spectrum and compare the results with the WMAP three year data. We find that our power spectrum gives a lower quadrupole anisotropy when $Ω-1 >0$, but matches the temperature anisotropy calculated from the standard Ratra-Peebles power spectrum at large $l$. The determination of spatial curvature from temperature anisotropy data is not much affected by the different power spectra which arise from the choice of different boundary conditions for the inflaton perturbation.

astro-ph↗

arXiv2006

Enhanced polarization of CMB from thermal gravitational waves

If inflation was preceded by a radiation era then at the time of inflation there will exist a decoupled thermal distribution of gravitons. Gravitational waves generated during inflation will be amplified by the process of stimulated emission into the existing thermal distribution of gravitons. Consequently the usual zero temperature scale invariant tensor spectrum is modified by a temperature dependent factor. This thermal correction factor amplify the $B$-mode polarization of the CMB by an order of magnitude at large angles, which may now be in the range of observability of WMAP.

astro-ph↗