MCMC analysis of WMAP3 and SDSS data points to broken symmetry inflaton potentials and provides a lower bound on the tensor to scalar ratio

TL;DR

The paper tests single-field slow-roll inflation within a Ginsburg–Landau-inspired trinomial potential using MCMC fits to WMAP3+LSS data, enforcing analytic $n_s$ and $r$ relations at order $1/N$. It finds strong evidence for breaking the $ ilde heta \to -\tilde heta$ symmetry, with trinomial new inflation providing the best description and a robust lower bound on $r$, while chaotic trinomial inflation is confined to a narrow region near the boundary of parameter space. The most probable new-inflation parameters yield $n_s \approx 0.956$ and $r \approx 0.055$, consistent with a detectable tensor component in near-future data, and the results favor a double-well-like potential in the viable models. Overall, the GL EFT trinomial approach offers a stable, physically motivated description of the data and highlights symmetry breaking as a key feature of the inflationary potential.

Abstract

We perform a MCMC (Monte Carlo Markov Chains) analysis of the available CMB and LSS data (including the three years WMAP data) with single field slow-roll new inflation and chaotic inflation models. We do this within our approach to inflation as an effective field theory in the GinsburgLandau spirit with fourth degree trinomial potentials in the inflaton field phi.We derive explicit formu- lae and study in detail the spectral index ns of the adiabatic fluctuations the ratio r of tensor to scalar fluctuations and the running index dn_s/dln k. We use these analytic formulas as hard constraints on n_s and r in the MCMC analysis.Our analysis differs in this crucial aspect from previous MCMC studies in the literature involving the WMAP3 data. Our results are as follow: (i) The data strongly indicate the breaking (whether spontaneous or explicit) of the phi -> -phi symmetry of the inflaton potentials both for new and for chaotic inflation.(ii)Trinomial new inflation naturally satisfies this requirement and provides an excellent fit to the data.(iii)Trinomial chaotic inflation produces the best fit in a very narrow corner of the parameter space.(iv) The chaotic symmetric trinomial potential is almost certainly ruled out(at 95% CL).In tri- nomial chaotic inflation the MCMC runs go towards a potential in the boundary of the parameter space and which ressembles a spontaneously symmetry broken potential of new inflation. (v) The above results and further physical analysis here lead us to conclude that new inflation gives the best description of the data.(vi) We find a lower bound for r within trinomial new inflation potentials r > 0.016 (95% CL) and r > 0.049 (68% CL). (vii) The preferred new inflation trinomial potential is a double well, even function of the field yielding as most probable values: n_s ~ 0.958, r ~ 0.055. Such r could be observed soon.

Figures (9)

• Figure 1: Trinomial Chaotic Inflation. We plot here the chaotic inflation trinomial potential [eq.(\ref{['trinoC']}) with positive quadratic term] $\frac{y}{8} \; w(\chi)$ vs. the field variable $\sqrt{z}=\sqrt{y/8} \; \chi$ for different values of the asymmetry parameter $h$, namely, $h =0, \; -0.5, \; -0.8$ and $-1$. Notice the inflection point at $\sqrt{z}= 1$ when $h=-1$.
• Figure 2: Trinomial Inflation. We plot $r$ vs. $n_s$ for fixed values of the asymmetry parameter $h$ and the field $z$ varying along the curves. The red curves are those of chaotic inflation with $h\le 0$ (only the short magenta curve has positive $h$), while the black curves are for new inflation. The color--filled areas correspond to $12\%, \; 27\%, \; 45\%, \; 68 \%$ and $95 \%$ confidence levels according to the WMAP3 and Sloan data. The color of the areas goes from the darker to the lighter for increasing CL. New inflation only covers a narrow area between the black lines while chaotic inflation covers a much wider area but, as shown by fig. \ref{['pdfzh']}, this wide area is only a small corner of the field $z$ - asymmetry $h$ plane. Since new inflation covers the banana-shaped region between the black curves, we see from this figure that the most probable values of $r$ are definitely non-zero within trinomial new inflation. Precise lower bounds for $r$ are derived from MCMC in eq.(\ref{['cotinfr']}).
• Figure 3: Trinomial New Inflation. The new inflation trinomial potential $\frac{y \; w(\chi)}{8 \; (h^2 + 1)^2}$ [eq.(\ref{['trino']})] vs. the field variable $\frac{\sqrt{y} \; \chi}{\sqrt{8} \; \sqrt{h^2 + 1}}$ for different values of the asymmetry parameter $h = 0, -0.4, -1, -20$. We have normalized here the field variable and the potential by $h$-dependent factors in order to have a smooth $|h| \gg 1$ limit.
• Figure 4: Comparison of the marginalized probability distributions (normalized to have maximum equal to one) of the most relevant cosmological parameters (both primary and derived) between Trinomial New Inflation (solid blue curves) and the $\Lambda$CDM+$r$ model (dashed red curves).
• Figure 5: Upper panels: 95% and 68% percent contour plots of joint probability $(\tau,n_s)$ distribution (left) and $(\tau,r)$ distribution (right) in the $\Lambda$CDM+$r$ model. Lower panels: the two joint distributions in trinomial new inflation. Recall that in this case $n_s < 0.9615\ldots$ is a theoretical bound when $N=50$.