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Register a new userCosmological consequences of a scalar field with oscillating equation of state. III. Unifying inflation with dark energy and small tensor-to-scalar ratio
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We investigate the inflationary consequences of the oscillating dark energy model proposed by Tian [href{https://doi.org/10.1103/PhysRevD.101.063531}{Phys. Rev. D {bf 101}, 063531 (2020)}], which aims to solve the cosmological coincidence problem with multi-accelerating Universe (MAU). We point out that the inflationary dynamics belong to slow-roll inflation. The spectral index of scalar perturbations and the tensor-to-scalar ratio $r$ are shown to be consistent with current textit{Planck} measurements. Especially, this model predicts $rsim10^{-7}$, which is far below the observation limits. This result motivates us to explore the smallness of $r$ in the general MAU. We propose a quintessential generalization of the original model and prove $r<0.01$ in general. The null detection to date of primordial gravitational waves provides a circumstantial evidence for the MAU. After the end of inflation, the scalar field rolls toward infinity instead of a local minimum, and meanwhile its equation of state is oscillating with an average value larger than $1/3$. In this framework, we show that gravitational particle creation at the end of inflation is capable of reheating the Universe.
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We take a pragmatic, model independent approach to single field slow-roll canonical inflation by imposing conditions, not on the potential, but on the slow-roll parameter $epsilon(phi)$ and its derivatives $epsilon^{prime }(phi)$ and $epsilon^{primeprime }(phi)$, thereby extracting general conditions on the tensor-to-scalar ratio $r$ and the running $n_{sk}$ at $phi_{H}$ where the perturbations are produced, some $50$ $-$ $60$ $e$-folds before the end of inflation. We find quite generally that for models where $epsilon(phi)$ develops a maximum, a relatively large $r$ is most likely accompanied by a positive running while a negligible tensor-to-scalar ratio implies negative running. The definitive answer, however, is given in terms of the slow-roll parameter $xi_2(phi)$. To accommodate a large tensor-to-scalar ratio that meets the limiting values allowed by the Planck data, we study a non-monotonic $epsilon(phi)$ decreasing during most part of inflation. Since at $phi_{H}$ the slow-roll parameter $epsilon(phi)$ is increasing, we thus require that $epsilon(phi)$ develops a maximum for $phi > phi_{H}$ after which $epsilon(phi)$ decrease to small values where most $e$-folds are produced. The end of inflation might occur trough a hybrid mechanism and a small field excursion $Deltaphi_eequiv |phi_H-phi_e |$ is obtained with a sufficiently thin profile for $epsilon(phi)$ which, however, should not conflict with the second slow-roll parameter $eta(phi)$. As a consequence of this analysis we find bounds for $Delta phi_e$, $r_H$ and for the scalar spectral index $n_{sH}$. Finally we provide examples where these considerations are explicitly realised.
The fact that fast oscillating homogeneous scalar fields behave as perfect fluids in average and their intrinsic isotropy have made these models very fruitful in cosmology. In this work we will analyse the perturbations dynamics in these theories assuming general power law potentials $V(phi)=lambda vertphivert^{n}/n$. At leading order in the wavenumber expansion, a simple expression for the effective sound speed of perturbations is obtained $c_{text{eff}}^2 = omega=(n-2)/(n+2)$ with $omega$ the effective equation of state. We also obtain the first order correction in $k^2/omega_{text{eff}}^2$, when the wavenumber $k$ of the perturbations is much smaller than the background oscillation frequency, $omega_{text{eff}}$. For the standard massive case we have also analysed general anharmonic contributions to the effective sound speed. These results are reached through a perturbed version of the generalized virial theorem and also studying the exact system both in the super-Hubble limit, deriving the natural ansatz for $deltaphi$; and for sub-Hubble modes, exploiting Floquets theorem.
The form of the inflationary potential is severely restricted if one requires that it be natural in the technical sense, i.e. terms of unrelated origin are not required to be correlated. We determine the constraints on observables that are implied in such natural inflationary models, in particular on $r$, the ratio of tensor to scalar perturbations. We find that the naturalness constraint does not require $r$ to be lare enough to be detectable by the forthcoming searches for B-mode polarisation in CMB maps. We show also that the value of $r$ is a sensitive discriminator between inflationary models.
In a recent work, we had constructed a model consisting of two fields---a canonical scalar field and a non-canonical ghost field---that had sourced a symmetric matter bounce scenario. The model had involved only one parameter, viz. the scale associated with the bounce. For a suitable value of the parameter, the model had led to strictly scale invariant power spectra with a COBE normalized scalar amplitude and a rather small tensor-to-scalar ratio. In this work, we extend the model to achieve near-matter bounces, which contain a second parameter apart from the bounce scale. As the new model does not seem to permit analytical evaluation of the scalar modes near the bounce, with the aid of techniques which we had used in our earlier work, we compute the scalar and the tensor power spectra numerically. For appropriate values of the additional parameter, we find that the model produces red spectra with a scalar spectral tilt and a small tensor-to-scalar ratio which are consistent with the recent observations of the anisotropies in the cosmic microwave background by Planck.
This paper aims to put constraints on the parameters of the Scalar Field Dark Matter (SFDM) model, when dark matter is described by a free real scalar field filling the whole Universe, plus a cosmological constant term. By using a compilation of 51 $H(z)$ data and 1048 Supernovae data from Panteon, a lower limit for the mass of the scalar field was obtained, $m geq 5.1times 10^{-34} $eV and $H_0=69.5^{+2.0}_{-2.1}text{ km s}^{-1}text{Mpc}^{-1}$. Also, the present dark matter density parameter was obtained as $Omega_phi = 0.230^{+0.033}_{-0.031}$ at $2sigma$ confidence level. The results are in good agreement to standard model of cosmology, showing that SFDM model is viable in describing the dark matter content of the universe.
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