Primordial Magnetic Fields and Curvature Perturbations in Pure Ultra Slow Roll Inflation
Core Concepts
In pure ultra slow roll inflation, suitable nonconformal coupling functions can lead to scaleinvariant primordial magnetic fields. The threepoint crosscorrelation between the curvature perturbations and magnetic fields exhibits interesting behavior, with the consistency condition governing the squeezed limit being violated.
Abstract
The content discusses the generation of primordial magnetic fields during pure ultra slow roll inflation. Key points:

In pure ultra slow roll inflation, the first slowroll parameter ε1 decreases rapidly, leading to a nearly constant Hubble parameter. This poses challenges in generating observable magnetic fields, as the nonconformal coupling function becomes nearly constant, restoring conformal invariance.

To overcome this, the authors consider a nonconformal coupling function that depends on the kinetic energy of the inflaton. They show that for suitable choices of parameters, this can lead to a scaleinvariant spectrum for the magnetic fields.

The authors then derive the thirdorder action describing the interaction between the curvature perturbations and the electromagnetic field. This allows them to compute the threepoint crosscorrelation between the curvature perturbations and the magnetic fields.

In pure ultra slow roll inflation, the curvature perturbations continue to grow on superHubble scales, leading to a violation of the standard consistency condition governing the scalar bispectrum. The authors investigate whether a similar violation occurs for the threepoint crosscorrelation between the curvature perturbations and magnetic fields.
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Crosscorrelation between the curvature perturbations and magnetic fields in pure ultra slow roll inflation
Stats
The Hubble parameter H is nearly constant during pure ultra slow roll inflation.
The first slowroll parameter ε1 behaves as ε1 ∝ a^(p), where p > 3.
The nonconformal coupling function J is chosen to be J ∝ (ε1/ε1e)^(n/2), where ε1e is the value of ε1 at the end of inflation.
Quotes
"To generate cosmological magnetic fields of observable strengths today, the conformal invariance of the electromagnetic action must be broken during inflation."
"In single field models of inflation admitting a phase of ultra slow roll, there arises a challenge in generating magnetic fields of observable strengths over large scales."
Deeper Inquiries
How would the threepoint crosscorrelation between curvature perturbations and magnetic fields be affected in models of inflation involving multiple fields?
In models of inflation involving multiple fields, the threepoint crosscorrelation between curvature perturbations and magnetic fields can exhibit significant modifications compared to singlefield models. The presence of additional scalar fields can introduce new interaction terms in the effective action, leading to a richer structure in the correlation functions. Specifically, the dynamics of the additional fields can alter the evolution of the curvature perturbations and the electromagnetic fields, potentially enhancing or suppressing the crosscorrelation.
One key aspect is that multiple fields can lead to more complex nonconformal coupling functions, which may depend on the kinetic energies of all the fields involved. This can result in a variety of behaviors for the magnetic field spectra, including different spectral tilts and amplitudes. The interplay between the fields can also lead to enhanced nonGaussianities, as the interactions can generate additional contributions to the threepoint functions. Consequently, the crosscorrelation may not only reflect the dynamics of the curvature perturbations but also the interactions among the multiple fields, leading to a more intricate relationship between the curvature perturbations and the magnetic fields.
What are the potential observational signatures of the violation of the consistency condition in the threepoint crosscorrelation, and how could they be detected?
The violation of the consistency condition in the threepoint crosscorrelation between curvature perturbations and magnetic fields can manifest in several potential observational signatures. One of the most significant implications is the presence of enhanced nonGaussianities in the primordial perturbations. In scenarios where the consistency condition is violated, the threepoint correlation functions may exhibit a distinct dependence on the wave numbers involved, particularly in the squeezed limit where one wave number is much smaller than the others.
These signatures could be detected through precise measurements of the cosmic microwave background (CMB) anisotropies and polarization. Specifically, the nonGaussianities can leave imprints on the temperature and polarization power spectra of the CMB, which can be analyzed using techniques such as bispectrum analysis. Additionally, future observations of largescale structure and galaxy clustering may reveal correlations that deviate from the predictions of standard inflationary models, providing further evidence of the underlying nonGaussianities.
Moreover, the detection of primordial gravitational waves, which are also influenced by the magnetic fields generated during inflation, could serve as a complementary probe. If the threepoint crosscorrelation exhibits significant deviations from the expected consistency condition, it may lead to observable effects in the gravitational wave spectrum, particularly in the context of tensor perturbations.
What are the broader implications of the continued growth of curvature perturbations on superHubble scales in pure ultra slow roll inflation for our understanding of the early universe?
The continued growth of curvature perturbations on superHubble scales during pure ultra slow roll inflation has profound implications for our understanding of the early universe. This behavior challenges the conventional wisdom associated with slow roll inflation, where perturbations are expected to freeze on superHubble scales. Instead, the growth of curvature perturbations suggests that the dynamics of the inflaton field can lead to significant deviations from the standard inflationary paradigm.
One major implication is the potential for generating a highly nonGaussian spectrum of primordial perturbations, which could have observable consequences in the CMB and largescale structure. The enhanced nonGaussianities may provide a unique signature of ultra slow roll inflation, allowing for the differentiation between various inflationary models based on their statistical properties.
Additionally, the growth of curvature perturbations raises questions about the stability of the inflationary phase and the subsequent evolution of the universe. It suggests that the transition from inflation to the radiationdominated era may be more complex than previously thought, potentially involving mechanisms that can amplify perturbations and lead to the formation of structures such as primordial black holes.
Overall, the implications of continued growth in curvature perturbations during pure ultra slow roll inflation extend beyond theoretical considerations, influencing our understanding of cosmic structure formation, the nature of dark matter, and the initial conditions of the universe. This highlights the importance of exploring nonstandard inflationary scenarios to gain deeper insights into the fundamental processes that shaped the early universe.