We propose a new way to implement an inflationary prior to a cosmological dataset that incorporates the inflationary observables at arbitrary order. This approach employs an exponential form for the Hubble parameter $H(ϕ)$ without taking the slow-roll approximation. At lowest non-trivial order, this $H(ϕ)$ has the unique property that it is the solution to the brachistochrone problem for inflation.
The observational data on the anisotropy of the cosmic microwave background constraints the scalar spectral tilt $n_s$ and the tensor to scalar ratio $r$ which depend on the first and second derivatives of the inflaton potential. The information can be used to reconstruct the inflaton potential in the polynomial form up to some orders. However, for some classes of potentials, $n_s$ and $r$ behave as $n_s(N)$ and $r(N)$ universally in terms of the number of e-folds $N$. The universal behaviour of $n_s(N)$ can be used to reconstruct a class of inflaton potentials. By parametrizing one of the par…
In this paper, we considered an inflationary model that effectively behaves as a modified Chaplygin gas in the context of quintessence cosmology. We reconstructed the inflaton potential bottom-up and using the recent observational data we fixed the free parameters of the model. We showed that the modified Chaplygin gas inspired model is suitable for both the early and the late time acceleration but has shortcomings between the two periods.
Recent cosmological observations are in good agreement with the scalar spectral index $n_s$ with $n_s-1\sim -2/N$, where $N$ is the number of e-foldings. Quadratic chaotic model, Starobinsky model and Higgs inflation or $α$-attractors connecting them are typical examples predicting such a relation. We consider the problem in the opposite: given $n_s$ as a function of $N$, what is the inflaton potential $V(ϕ)$. We find that for $n_s-1=-2/N$, $V(ϕ)$ is either $\tanh^2(γϕ/2)$ ("T-model") or $ϕ^2$ (chaotic inflation) to the leading order in the slow-roll approximation. $γ$ is the ratio of $1/V$ at…
We suggest a new method to reconstruct, within canonical single-field inflation, the inflaton potential directly from the primordial power spectrum which may deviate significantly from near scale-invariance. Our approach relies on a more generalized slow-roll approximation than the standard one, and can probe the properties of the inflaton potential reliably. We give a few examples for reconstructing potential and discuss the validity of our method.
The coupling between spin and torsion in the Einstein-Cartan-Sciama-Kibble theory of gravity generates gravitational repulsion at very high densities, which prevents a singularity in a black hole and may create there a new universe. We show that quantum particle production in such a universe near the last bounce, which represents the Big Bang gives the dynamics that solves the horizon, flatness, and homogeneity problems in cosmology. For a particular range of the particle production coefficient, we obtain a nearly constant Hubble parameter that gives an exponential expansion of the universe wi…
In this short paper we outline a recipe for the reconstruction of $F(R)$ gravity starting from single field inflationary potentials in the Einstein frame. For simple potentials one can compute the explicit form of $F(R)$, whilst for more involved examples one gets a parametric form of $F(R)$. The $F(R)$ reconstruction algorithm is used to study various examples: power-law $ϕ^n$, exponential and $α$-attractors. In each case it is seen that for large $R$ (corresponding to large value of inflaton field), $F(R) \sim R^2$. For the case of $α$-attractors $F(R) \sim R^2$ for all values of inflaton fi…
With the recently published Cosmic Microwave Background data from Planck we address the optimized binning of the primordial power spectrum. As an important modification to the usual binning of the primordial spectrum, along with the spectral amplitude of the bins, we allow the position of the bins also to vary. This technique enables us to address the location of the possible broad physical features in the primordial spectrum with relatively smaller number of bins compared to the analysis performed earlier. This approach is in fact a reconstruction method looking for broad features in the prim…
Bulk dark energy properties are determined by the redshift evolution of its pressure-to-density ratio, $w_{de}(z)$. An experimental goal is to decide if the dark energy is dynamical, as in the quintessence (and phantom) models treated here. We show that a three-parameter approximation $w_{de}(z; ε_s, ε_{ϕ\infty}, ζ_s)$ fits well the ensemble of trajectories for a wide class of late-inflaton potentials $V(ϕ)$. Markov Chain Monte Carlo probability calculations are used to confront our $w_{de}(z)$ trajectories with current observational information on Type Ia supernova, Cosmic Microwave Backgroun…
We investigate to which extent and under which circumstances false vacuum energy ($V_0$) dominated slow-roll inflation is compatible with a large tensor-to-scalar ratio $r = O(0.1)$, as indicated by the recent BICEP2 measurement. With $V_0$ we refer to a constant contribution to the inflaton potential, present before a phase transition takes place and absent in the true vacuum of the theory, like e.g. in hybrid inflation. Based on model-independent considerations, we derive an upper bound on the possible amount of $V_0$ domination and highlight the importance of higher-order runnings of the sc…
The reconstruction of a k-essence inflationary universe, considering the unification between the swampland criteria and the attractor given by the scalar spectral index $n_S(N)$ together with the slow roll parameter $ε(N)$in terms of the number of $e$-folds $N$ is studied. In the context of a coupling of the form $L(ϕ)\,X$ in the k-essence model, we find the effective potential $V$ and the coupling parameter $L$ in terms of the scalar spectral index and the slow roll parameter under a general formalism. To apply the unification in our model, we consider some examples in order to rebuild the ef…
A possible origin of the anomalous dip and bump in the primordial power spectrum, which are reconstructed from WMAP data corresponding to the multipole $\ell=100\sim 140$ by using the inversion method, is investigated as a consequence of modification of scalar field dynamics in the inflation era. Utilizing an analytic formula to handle higher order corrections to the slow-roll approximation, we evaluate the relation between a detailed shape of inflaton potential and a fine structure in the primordial power spectrum. We conclude that it is unlikely to generate the observed dip and bump in the p…
In this paper we will analyse the constraints on a sub-Planckian excursion of a single inflaton field, which would yield a large tensor to scalar ratio, while explaining the temperature anisotropy of the cosmic microwave background (CMB) radiation. In particular, our attempt will be to reconstruct the inflationary potential by constraining, $V(ϕ_0), V^{\prime}(ϕ_0), V^{\prime\prime}(ϕ_0), V^{\prime\prime\prime}(ϕ_0)$ and $V^{\prime\prime\prime\prime}(ϕ_0)$, in the vicinity of the field, $ϕ_0\ll M_p$, and the field displacement, $Δϕ\ll M_p$, where $M_p$ is the reduced Planck mass. We will provi…
We use a mathematical approach based on the constraints systems in order to reconstruct the equation of state and the inflationary potential for the inflaton field from the observed spectral indices for the density perturbations $n_{s}$ and the tensor to scalar ratio $r$. From the astronomical data, we can observe that the measured values of these two indices lie on a two-dimensional surface. We express these indices in terms of the Hubble slow-roll parameters and we assume that $n_{s}-1=h\left( r\right) $. For the function $h\left( r\right) $, we consider three cases, where $h\left( r\right) …
In this paper my prime objective is to analyze the constraints on a sub-Planckian excursion of a single inflaton field within Effective Field Theory framework in a model independent fashion. For a generic single field inflationary potential, using the various parameterization of the primordial power spectrum I have derived the most general expression for the field excursion in terms of various inflationary observables, applying the observational constraints obtained from recent Planck 2015 and Planck 2015 +BICEP2/Keck Array data. By explicit computation I have reconstructed the structural form…
Determination of whether the Harrison--Zel'dovich spectrum for primordial scalar perturbations is consistent with observations is sensitive to assumptions about the reionization scenario. In light of this result, we revisit constraints on inflationary models using more general reionization scenarios. While the bounds on the tensor-to-scalar ratio are largely unmodified, when different reionization schemes are addressed, hybrid models are back into the inflationary game. In the general reionization picture, we reconstruct both the shape and amplitude of the inflaton potential. We find a broader…
