# Perturbation spectrum after inflation

• smallphi
In summary, the spectrum of perturbations at the end of inflation is calculated under the assumption that each perturbation mode crosses some initial time in the comoving coordinates with 'minimum energy allowed by the Heisenberg uncertainty principle'. The spectrum can change if the initial conditions of the modes are changed, but the use of comoving coordinates does not violate the principle of general covariance in GR.
smallphi
The spectrum of perturbations at the end of inflation, which turns out to be flat and slightly red shifted, is calculated under the assumption that each perturbation mode crosses some initial time in the comoving coordinates with 'minimum energy allowed by the Heisenberg uncertainty principle'.

Does the spectrum change if the initial conditions of the modes are changed?

Isn't using the comoving coordinates in violation of the principle of general covariance in GR i. e. it singles out a preferred frame to calculate 'physical observables'?

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Yes, the spectrum can change if the initial conditions of the modes are changed. However, the Heisenberg uncertainty principle still applies in this case and provides a constraint on the initial conditions of the perturbation modes. The use of comoving coordinates is not a violation of the principle of general covariance in GR, as comoving coordinates are just a choice of coordinates used to describe the spacetime. These coordinates provide a convenient way to calculate physical observables, but do not single out a preferred frame.

## 1. What is the perturbation spectrum after inflation?

The perturbation spectrum after inflation refers to the distribution of fluctuations in the density and temperature of the early universe that were generated during the inflationary period. These perturbations are considered the seeds for the formation of large-scale structures in the universe, such as galaxies and galaxy clusters.

## 2. How is the perturbation spectrum after inflation measured?

The perturbation spectrum after inflation is measured using observations of the cosmic microwave background (CMB) radiation. This radiation is the oldest light in the universe and carries information about the early universe, including the density and temperature fluctuations that were generated during inflation. Scientists use sophisticated instruments such as the Planck satellite to measure the CMB and determine the perturbation spectrum.

## 3. What does the perturbation spectrum after inflation tell us about the early universe?

The perturbation spectrum after inflation provides valuable insights into the conditions of the early universe. It can tell us about the energy scale and duration of inflation, the nature of the inflaton field responsible for inflation, and the size and shape of the universe. It also helps us understand the origins of the large-scale structures we see in the universe today.

## 4. How does the perturbation spectrum after inflation support the theory of cosmic inflation?

The perturbation spectrum after inflation is a key piece of evidence that supports the theory of cosmic inflation. The theory predicts a specific pattern of fluctuations in the CMB, which aligns with the observations of the perturbation spectrum. Additionally, the theory explains why the universe appears to be flat and homogeneous on large scales, which is also supported by the perturbation spectrum.

## 5. Can the perturbation spectrum after inflation be used to test other theories of the universe?

Yes, the perturbation spectrum after inflation can be used to test and constrain other theories of the universe, such as alternative inflation models or theories of dark matter and dark energy. By comparing the predictions of these theories to the observations of the perturbation spectrum, scientists can determine which theories are most consistent with the data and refine our understanding of the early universe.

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