Constraining tachyonic inflationary β-exponential model with Continuous Spontaneous Localization collapse scheme

TL;DR

This paper studies tachyonic inflation with a $β$-exponential potential under a Continuous Spontaneous Localization (CSL) collapse scheme. It derives how CSL modifies the scalar power spectrum, leading to corrections in the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$ through the collapse parameter $α$ and the potential parameter $β$. By confronting Planck 2018, BK18+BAO, and ACT DR6 data, it constrains $α$ and $β$, finding that CSL generally relaxes the $β$-exponential bounds while remaining consistent with observations; turning off CSL recovers the standard predictions. The work demonstrates that CSL can imprint observable signatures in the CMB and motivates applying CSL analyses to other tachyonic inflationary setups to further probe quantum-to-classical transitions in the early Universe.

Abstract

In this work, we consider the dynamics of the self-induced collapse of the tachyon wave function in inflationary scenarios. We analyze the modifications on the power spectrum by considering the $β$-exponential potential, whose parameters have updated constraints by the Planck 2018 baseline data and recent results from the Atacama Cosmology Telescope (ACT). Moreover, we show that for this kind of potential, just for a narrow range of $β$-parameter, there is agreement between the theoretical predictions and the current observational data. Considering the proposal for a collapse scheme that leads to the modification of Schrödinger evolution of the inflation wave function from the employment of a Continuous Spontaneous Localization (CSL) approach, we derive the scalar spectral index and tensor-to-scalar ratio. We then obtained the constraints on both collapse and $β$-parameters that, in turn, yield deviations in the $n_{s}$ vs. $r$ plane when compared to the $β$-exponential potential standard estimate. The CSL scheme applied to tachyonic inflation driven by a $β$-potential offers an adequate description of the recent data.

Figures (4)

• Figure 1: The potential $V(T)$ as a function of the tachyon field $T$ is shown to some $\beta$-values.
• Figure 2: The marginalized joint regions at $68\%$ and $95\%$ confidence levels for the spectral index ($n_{s}$) and tensor-to-scalar ratio ($r$) derived from Planck data (independently and combined with BK18+BAO) PLANCK2018 and Atacama Cosmology Telescope (combined with other datasets) calabrese2025atacamacosmologytelescopedr6 are compared to the theoretical predictions of the tachyonic inflationary $\beta$-exponential model. The number of e-folds have been fixed at $N=50$ and $N=60$.
• Figure 3: In the context of the CSL inflationary model, the function $\mathcal{F}(\lambda_{k},\nu_{s})$ is associated with the power spectrum. The parameters $\lambda_{0}$ (set at $1/\left|\tau\right|=1.03\times10^{-5}\mathrm{Mpc^{-1}}$) and $\mu$ (fixed at 0.5), remain constant.
• Figure 4: The $n_{s}-r$ plane for the $\beta$-exponential potential is shown for different values of $\alpha$ and $\beta$. The standard tachyon inflation is recovered by assuming $\alpha=0$, while $\alpha\neq0$ introduces the CSL inflationary model deviations, which changes the behavior of the standard spectral index. Two values for the number of e-folds, $N=50$ (dashed lines) and $N=60$ (dash-dotted curves), are considered.