Inflationary Magnetogenesis in $R^2$-Inflation after Planck 2015

Abstract

We study the primordial magnetic field generated by the simple model $f^{2}FF$ in Starobinsky, $R^2$-inflationary, model. The scale invariant PMF is achieved at relatively high power index of the coupling function, $\left|\alpha \right|\approx 7.44$. This model does not suffer from the backreaction problem as long as, the rate of inflationary expansion, $H$, is in the order of or less than the upper bound reported by Planck ($\le 3.6 \times 10^{-5} M_\rm{Pl}$) in both de Sitter and power law expansion, which show similar results. We calculate the lower limit of the reheating parameter, $R_\rm{rad} > 6.888$ in $R^2$-inflation. Based on the upper limit obtained from CMB, we find that the upper limits of magnetic field and reheating energy density as, $\left(ρ_{B_\rm{end}} \right)_\rm{CMB} < 1.184 \times 10^{-20} M_\rm{Pl}^4$ and $\left(ρ_\rm{reh} \right)_\rm{CMB} < 8.480 \times 10^{-22} M_\rm{Pl}^4$. All of foregoing results are well more than the lower limit derived from WMAP7 for both large and small field inflation. By using the Planck inflationary constraints, 2015 in the context of $R^2$-inflation, the upper limit of reheating temperature and energy density for all possible values of $w _\rm{reh}$ are respectively constrained as, $T_\rm{reh} < 4.32 \times 10^{13} \rm{GeV}$ and $ρ_\rm{reh} < 3.259 \times 10^{-18} M_\rm{Pl}^4$ at $n_\rm{s} \approx 0.9674$. This value of spectral index is well consistent with Planck, 2015 results. Adopting $T_\rm{reh}$, enables us to constrain the reheating e-folds number, $N_\rm{reh}$ on the range $1 < N_\rm{reh} < 8.3$, for $- 1/3 < w_\rm{reh} < 1$. By using the scale invariant PMF generated by $f^{2}FF$, we find that the upper limit of present magnetic field, $B_0<8.058\times 10^{-9}\mathrm{G}$.

arXiv comment25 pages, 13 figures, Prepared for submission to JCAP

References in corpus (33)

• The Standard Model Higgs boson as the inflaton
• Towards the Theory of Reheating After Inflation
• BICEP2 I: Detection Of B-mode Polarization at Degree Angular Scales
• Three Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Polarization Analysis
• Magnetic Fields in the Early Universe
• Inflation Dynamics and Reheating
• A Joint Analysis of BICEP2/Keck Array and Planck Data
• Origin of Galactic and Extragalactic Magnetic Fields
• Cosmological Magnetic Fields: Their Generation, Evolution and Observation
• Formalising the Slow-Roll Approximation in Inflation
• How long before the end of inflation were observable perturbations produced?
• Primordial magnetogenesis
• First CMB Constraints on the Inflationary Reheating Temperature
• Particle physics models of inflation and curvaton scenarios
• Generation of Large-Scale Magnetic Fields in Single-Field Inflation
• Damping of Cosmic Magnetic Fields
• Inflation after WMAP3: Confronting the Slow-Roll and Exact Power Spectra with CMB Data
• Cosmology with inhomogeneous magnetic fields
• Equation-of-State Parameter for Reheating
• Parametric Amplification of Gravitational Fluctuations During Reheating
• Determination of intergalactic magnetic fields from gamma ray data
• Parametric Amplification of Metric Fluctuations During Reheating in Two Field Models
• General Relativistic effects in preheating
• Magnetic fields in the Large-Scale Structure of the Universe
• Planck intermediate results. XXXIII. Signature of the magnetic field geometry of interstellar filaments in dust polarization maps
• Inflationary Magnetogenesis without the Strong Coupling Problem II: Constraints from CMB anisotropies and B-modes
• The precision of slow-roll predictions for the CMBR anisotropies
• Correlation of inflation-produced magnetic fields with scalar fluctuations
• Primordial Magnetic Field Limits from Cosmic Microwave Background Bispectrum of Magnetic Passive Scalar Modes
• Non-Gaussian features of primordial magnetic fields in power-law inflation
• Magneto-reheating constraints from curvature perturbations
• Constraint on the primordial vector mode and its magnetic field generation from seven-year Wilkinson Microwave Anisotropy Probe Observations
• Stringent magnetic field limits from early universe dynamos cosmology with torsion

Cited by in corpus (2)

• Convergence and Stationary Distributions for Walsh Diffusions
• The Primordial Magnetic Field (PMF) Generated in Large Field Inflation (LFI), Natural Inflation (NI) and $R^2$-Inflation by $f^{2}FF$ Model