A novel way of constraining the α\alpha-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 $\alpha$-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 $\alpha$ parameter through microscopic calculations. Recent studies had already put model-dependent constraints on the values of $\alpha$ through the hyperbolic geometry of a Poincar\'{e} 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 $\alpha$ 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 $\alpha$ stated above, within $68\%$ CL. Moreover, we have calculated $r$ for some other possible values of $\alpha$ both in low-$\alpha$ limit, using the formula $r=\frac{12\alpha}{N^{2}}$, and in the high-$\alpha$ limit, using the formula $r=\frac{4n}{N}$, for $n=2$ and $4$. With all such values of $\alpha$, our calculated results match with the Planck-2018 data with $68\%$ or near $95\%$ CL.Comment: 41 pages, 29 figures, expanded the abstract, added figures and references, enlarged the discussio

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

We study the role of $\alpha$-parameter of the newly proposed model of quintessential $\alpha$-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 $0.28\leq\alpha\leq 0.30$. This range of $\alpha$ 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 $\alpha$ 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 $\alpha$-attractor.Comment: 38 pages, 11 figure

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 the Kähler potential arising from the large-volume scenario $(\alpha'^3)$ and four-graviton scattering amplitude up to 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 itself as an auxiliary field

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 (CY3). 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