arXiv subjects

Arunoday Sarkar

Publications and source records attributed to Arunoday Sarkar.

9 recordsLinked to original sources

arXiv2024

Constraining an Early Dark Energy Motivated Quintessential $α$-Attractor Inflaton Potential

We construct a new model of quintessential $α$ attractor inflation in conjunction with the features of non-oscillating early dark energy (EDE). Slow-roll plateau of this model is obtained, and analyzed in $k$-space, through the inflaton field and its first-order perturbation over a quasi de-Sitter metric fluctuation in the range $k=0.001-0.009$ Mpc$^{-1}$. The estimated cosmological parameters are found to obey Planck+BICEP2/Keck bounds with $68\%$ CL with the required trend of spectral tilts in the $n_s-r$ parametric space. We verify that, the inclusion of the EDE does not significantly affect the observed parameters. Its presence manifests in obtaining \textit{improved values} of the energy scale of inflation ($M$) and the present-day vacuum density ($V_Λ$). They are found to be $M=5.58\times 10^{-4}-4.57\times 10^{-3} M_P$ and $V_Λ=1.042\times 10^{-119}-4.688\times 10^{-116} M_P^4$. However, the $α$-parameter is drastically constrained in two ways. Its lower end is fixed by the consistency analysis of the $k$-mode equations, while the upper end is evaluated as a derived expression of $α$-cut-off through the aspects of EDE \textit{viz.,} the effects of \textit{Enhanced Symmetry Point} (ESP) in the potential during inflation. Improvised range of $α$ is found to be $0.001\leqα<0.1$ for the model parameters $γ$ and $n$ lying within $0.01\leqγ\leq 0.09$ and $8\leq n\leq 10$ respectively. These ranges are shown to be essential for satisfying the COBE/Planck normalized energy scale of inflation and the Planck-value of present-day vacuum density. If we choose $γ=0.0818$ and $n=8$, then we get $0.001\leqα\leq 0.0186$. Thus, the lower and upper limits of $α$ are diminished substantially, compared with those in the earlier studies.

gr-qc↗

arXiv2024

Spontaneous baryogenesis and generation of gravitational waves in a new model of quintessential $α$-attractor

We study the role of $α$-parameter of the newly proposed model of quintessential $α$-attractor inflation (arXiv: 2305.00230 [gr-qc]) to the case of quintessential spontaneous baryogenesis and generation of relic gravitational waves in presence of a rolling scalar field during kination. An \textit{effective 4-Fermi construct} technique has been employed to compute the freeze-out temperature and the baryon-to-entropy ratio, of which the obtained results conform to the experimental requirements for $0.28\leqα\leq 0.30$. This range of $α$ is found to originate from the functional behaviour of the end-value expression of the potential concerned. We also find a blue-tilted gravitational wave spectrum during a transition from inflation to kination. The amplitudes of the gravitational waves during radiation domination satisfy the constraint for nucleosynthesis and the characteristic strain of the ongoing gravitational wave detectors. Thus, the most important observation emerged from the present study is that, increasingly small fractional values of $α$ are favourable for unification of inflation, baryogenesis, quintessence and gravitational waves within a single model. This could have an interesting connection with the fundamental origin of $α$-attractor.

hep-th↗

arXiv2024

Inflationary $α$-Attractor From Type IIB/F Theory

We derive an $α=1/3$ - attractor potential of slow-roll inflation in the geometric set-up of three intersecting $D7$ branes under $T^6/Z_N$ type of $CY_3$-compactification within type IIB/F theory with some near-conifold regions. The underlying quadratic structure of the kinetic poles is found to arise from a correction in the Kähler potential when an extra contribution of open string moduli is turned on. While the closed string sector of the moduli spectrum is completely stabilized via quantum corrections of perturbative and non-perturbative origin, the open string sector plays the lead role in driving the inflationary expansion in the radial direction. A generic asymptotic behavior of the inflaton field near the pole boundaries manifests as the slow-roll plateau in canonical field space, which becomes responsible for giving universal predictions of the cosmological parameters. We find that the presence of the open strings near conifold regions brings the realization of pole inflation in the present set up. Finally we compare our results with similar models and discuss the importance of exploring precise values of $α$ in the light of ongoing and forthcoming cosmological surveys.

hep-th↗

arXiv2023

Non-perturbative stabilization of two Kähler moduli in type-IIB/F theory and the inflaton potential

We consider a combination of perturbative and non-perturbative corrections in Kähler moduli stabilizations in the configuration of three magnetised intersecting D7 branes in the type-IIB/F theory, compactified on the 6d T^6/Z_N orbifold of Calabi-Yau three-fold (CY_3). Two of the Kähler moduli are stabilized non-perturbatively, out of the three which get perturbative corrections up to one-loop-order multi-graviton scattering amplitudes in the large volume scenario. In this framework, the dS vacua are achieved through all Kähler moduli stabilizations by considering the D-term. We obtain inflaton potentials of slow-roll plateau-type, which are expected by recent cosmological observations. Calculations of cosmological parameters with the potentials yield experimentally favoured values.

gr-qc↗

arXiv2023

Constraining the quintessential $α$-attractor inflation through dynamical horizon exit method

In the present paper, we perform a sub-Planckian quantum mode analysis of linear cosmological perturbation in the inflaton field over a classical quasi de-Siter metric background by dynamical horizon exit (DHE) method. In this way, we probe the inflationary regime of a quintessential $α$-attractor model by analysing the COBE/Planck normalized power spectra, spectral indices, tensor to scalar ratio, number of e-folds, running of the spectral index and inflationary Hubble parameter in $k$-space. We compare our results with ordinary $α$-attractor $E$ and $T$ models and with that of Planck-2018 results. Our estimated values of $n_s$ and $r$ lie within $68\%$ CL with respect to Planck data for $k=0.001 - 0.009$ Mpc$^{-1}$ for all values of $α$. The $α$ values, obtained in our calculations satisfy various post inflationary constraints regarding preheating and reheating, reported in current literature. We observe that quintessence sets an upper bound of $α=4.3$ and thereby restricts the model from becoming of the power law type, making it more efficacious than ordinary $α$-attractors in explaining both inflation and dark energy. A striking observation in our analyses is that, unlike in our previous study, we find a continuous values of $α$ within $\frac{1}{10}\leq α\leq 4.3$ for the specified $k$ range. At the end, we have shown that the model parameters constrained in this work give a very small vacuum density $\sim 10^{-117}-10^{-115} M_P^4$ which is an essential criterion for current and future dark energy observations of the universe.

gr-qc↗

arXiv2022

Single field slow-roll effective potential from Kähler moduli stabilizations in type IIB/F-theory

We derive a single field slow-roll inflaton potential in three intersecting $D7$ branes configuration under type IIB/F-theory compactification. Among three resulting Kähler moduli corresponding to three orthogonal directions, two are stabilized via perturbative corrections in Kähler potential arising from large volume scenario ($α'^3$) and four graviton scattering amplitude upto one loop level and the remaining Kähler modulus is stabilized by KKLT-type non-perturbative correction in superpotential. The symmetric combination of two canonically normalized and perturbatively stabilized Kähler moduli gives the inflaton field and the anti-symmetric combination manifests as an auxiliary field.

hep-th↗

arXiv2022

Can breakdown of perturbation in the $α$-attractor inflation lead to PBH formation?

With the basic $α$-attractor potentials, we investigate an inflationary regime in the high-$k$ limit, where the cosmological perturbation breaks down due to large enhancement in the scalar power spectrum and generation of large negative values of the Bardeen potential. We analyze that, this deep sub-horizon regime creates a situation, which is congenial to the formation of the primordial black holes (PBHs). We work in the spatially flat gauge with $δϕ\neq$ 0 and thus explicitly show the roles of perturbations in the inflaton field as well as in the background gravitational field in the mentioned enhancements and thereby in the PBH formation. We calculate the values of $σ(M)$, $β(M)$ and $f_\mathrm{PBH}(M)$ around the peaks in the density contrast profile and thus estimate the fraction of PBH in the dark matter of the present universe, corresponding to certain mass scales. We observe the formation of PBHs in the $k$ range $0.43\times 10^{13}$ Mpc$^{-1}$ to $9.8\times 10^{13}$ Mpc$^{-1}$ with masses $1.35\times 10^{-13}M_\odot$ to $2.60\times 10^{-16}M_\odot$, evaporation times $7.74\times 10^{33}$ sec to $5.53\times 10^{25}$ sec, Hawking temperatures $3.72\times 10^{-8}$ GeV to $1.93\times 10^{-5}$ GeV and $f_\mathrm{PBH}(M)$ $\sim 6.12\times 10^{-6}$ to $3.63\times 10^{-1}$. The calculated mass range lies in the regions of forecasts by LISA, WD, NS, DECIGO/AI, FL, SIGWs and the $f_\mathrm{PBH} (M)$ results overlap with those of DECIGO/AI, FL, SIGWs.

gr-qc↗

arXiv2021

A novel way of constraining the $α$-attractor chaotic inflation through Planck data

Defining a scale of $k$-modes of the quantum fluctuations during inflation through the dynamical horizon crossing condition $k = aH$ we go from the physical $t$ variable to $k$ variable and solve the equations of cosmological first-order perturbations self consistently, with the chaotic $α$-attractor type potentials. This enables us to study the behaviour of $n_{s}$, $r$, $n_{t}$ and $N$ in the $k$-space. Comparison of our results in the low-$k$ regime with the Planck data puts constraints on the values of the $α$ parameter through microscopic calculations. Recent studies had already put model-dependent constraints on the values of $α$ through the hyperbolic geometry of a Poincaré disk: consistent with both the maximal supergravity model $\mathcal{N}=8$ and the minimal supergravity model $\mathcal{N}=1$, the constraints on the values of $α$ are $\frac{1}{3}$, $\frac{2}{3}$, 1, $\frac{4}{3}$, $\frac{5}{3}$, 2, $\frac{7}{3}$. The minimal $\mathcal{N}=1$ supersymmetric cosmological models with $B$-mode targets, derived from these supergravity models, predicted the values of $r$ between $10^{-2}$ and $10^{-3}$. Both in the $E$-model and the $T$-model potentials, we have obtained, in our calculations, the values of $r$ in this range for all the constrained values of $α$ stated above, within $68\%$ CL. Moreover, we have calculated $r$ for some other possible values of $α$ both in low-$α$ limit, using the formula $r=\frac{12α}{N^{2}}$, and in the high-$α$ limit, using the formula $r=\frac{4n}{N}$, for $n=2$ and $4$. With all such values of $α$, our calculated results match with the Planck-2018 data with $68\%$ or near $95\%$ CL.

gr-qc↗

arXiv2020

Mode analysis of cosmological perturbations with the $E$-model $α$-attractor inflaton potentials

We have carried out detailed $k$-mode analysis of single-inflaton slow-roll inflationary perturbations including quantum fluctuations by setting up non-linear coupled differential equations of inflaton field ($ϕ$), its perturbation ($δϕ$) and the metric perturbation (the Bardeen potential, $Φ_B$), and calculated the number of e-folds ($N$), scalar spectral index ($n_s$), tensor spectral index ($n_h$), scalar power spectrum ($Δ_s$), tensor power spectrum ($Δ_h$), tensor-to-scalar ratio ($r$) and the Hubble parameter ($H$) for different $k$ values at the horizon crossing. In these calculations we have employed the $E$-model $α$-attractor potentials which are found to display slow-roll behaviour. The values of $n_s$ and $r$ obtained by us are consistent with those given by the well-known universal $α$-attractor formulae. We got $n_s = 0.956908$ and $r= 0.005571 $ at $k = 10^6$ Planck unit for the value of the potential parameter $n = 1$. These can be compared with the Planck-2018 data viz., $n_s = 0.9649\pm 0.0042$ at $68\%$ CL, $r<0.064$ at $95\%$ CL and ACT-2020 data viz., $n_s = 0.9691\pm 0.0041$ at $68\%$ CL.

gr-qc↗