Single field inflation in the light of Pulsar Timing Array Data: Quintessential interpretation of blue tilted tensor spectrum through Non-Bunch Davies initial condition

Abstract

In this work, we present a quintessential interpretation of having a blue-tilted tensor power spectrum for canonical single-field slow-roll inflation to explain the recently observed Pulsar Timing Array (NANOGrav 15-year and EPTA) signal of Gravitational Waves (GW). We formulate the complete semi-classical description of cosmological perturbation theory in terms of scalar and tensor modes using the Non-Bunch Davies initial condition. We found that the existence of the blue tilt ($n_t$) within the favoured range $1.2<n_t<2.5$ can be explained in terms of a newly derived consistency relation. Further, we compute a new field excursion formula using the Non-Bunch Davies initial condition, that validates the requirement of Effective Field Theory in the sub-Planckian regime, $|\Delta \varphi |\ll M_{\mathrm{pl}}$ for the allowed value of the tensor-to-scalar ratio, $r<0.06$ from CMB observations. In our study, we refer to this result as Anti Lyth bound as it violates the well-known Lyth bound originally derived for Bunch Davies initial condition. Further, we study the behaviour of the spectral density of GW and the associated abundance with the frequency, which shows that within the frequency domain $10^{-9}\mathrm{Hz}<f<10^{-7}\mathrm{Hz}$ the outcome obtained from our analysis is completely consistent with the Pulsar Timing Array (NANOGrav 15-year and EPTA) signal. Also, we found that the behaviour of GW spectra satisfies the CMB constraints at the low frequency, $f_{\ast }\sim 7.7\times 10^{-17}\mathrm{Hz}$ corresponding to the pivots scale wave number, $k_{\ast }\sim 0.05{\mathrm{Mpc}}^{-1}$. Finally, the sharp falling behaviour of the GW spectra within the frequency domain $10^{-7}\mathrm{Hz}<f<1\mathrm{Hz}$ validates our theory in the comparatively high-frequency regime as well.

32 pages, 2 figures, Pulsar Timing Array (NANOGrav 15 and EPTA) centered paper, references updated, Comments are welcome, Title of the paper slightly changed by following Editor's request, Revised version accepted for publication in European Physical Journal C

References in corpus (34)

• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• Advanced LIGO
• The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background
• Search for an isotropic gravitational-wave background with the Parkes Pulsar Timing Array
• Searching for the nano-Hertz stochastic gravitational wave background with the Chinese Pulsar Timing Array Data Release I
• The NANOGrav 15-year Data Set: Search for Signals from New Physics
• The NANOGrav 15-year Data Set: Observations and Timing of 68 Millisecond Pulsars
• The International Pulsar Timing Array second data release: Search for an isotropic Gravitational Wave Background
• On the evidence for a common-spectrum process in the search for the nanohertz gravitational-wave background with the Parkes Pulsar Timing Array
• Gravitational wave stochastic background from cosmic (super)strings
• Reheating constraints to inflationary models
• Common-red-signal analysis with 24-yr high-precision timing of the European Pulsar Timing Array: Inferences in the stochastic gravitational-wave background search
• Eppur è piatto? The cosmic chronometer take on spatial curvature and cosmic concordance
• The gravitational-wave background null hypothesis: Characterizing noise in millisecond pulsar arrival times with the Parkes Pulsar Timing Array
• The NANOGrav 15-Year Data Set: Detector Characterization and Noise Budget
• Folded Resonant Non-Gaussianity in General Single Field Inflation
• Quintessential inflation with canonical and noncanonical scalar fields and Planck 2015 results
• Unification of inflation and dark energy {\it à la} quintessential inflation
• A class of quintessential inflation models with parameter space consistent with BICEP2
• Probing the Early Universe with Axion Physics and Gravitational Waves
• Bell violation in the Sky
• ${\varphi }^2$ or Not ${\varphi }^2$: Testing the Simplest Inflationary Potential
• Common-spectrum process versus cross-correlation for gravitational-wave searches using pulsar timing arrays
• Can Effective Field Theory of inflation generate large tensor-to-scalar ratio within Randall Sundrum single braneworld?
• Constraining $\mathcal{N}=1$ supergravity inflationary framework with non-minimal Kähler operators
• Footprints of Axion-Like Particle in Pulsar Timing Array Data and James Webb Space Telescope Observations
• Evading Lyth bound in models of quintessential inflation
• Inflation and Alternatives with Blue Tensor Spectra
• Evaluating the prevalence of spurious correlations in pulsar timing array datasets
• Constraining $\mathcal{N}=1$ supergravity inflation with non-minimal Kähler operators using $\delta N$ formalism
• The Cosmological OTOC: Formulating new cosmological micro-canonical correlation functions for random chaotic fluctuations in Out-of-Equilibrium Quantum Statistical Field Theory
• No evidence for the blue-tilted power spectrum of relic gravitational waves
• A Bouncing Cosmology from VECROs
• One-loop Corrections in Power Spectrum in Single Field Inflation

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