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Hybrid_Inflation.nb
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Hybrid_Inflation.nb
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(* Content-type: application/vnd.wolfram.mathematica *)
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Canonical Scalar Field Inflation In The Presence Of A Chern-Simons Term.\
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Hybrid Inflation With An Oscillating Chern-Simons Scalar Coupling Function.\
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1.Designation Of Scalar Functions, Equations Of Motion, Slow-Roll/Observed \
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We start by designating the scalar functions of the model. For simplicity, \
the Chern-Simons scalar coupling function obtains a trigonometric form and \
the scalar field a power-law form. Compatibility is achieved for a quadratic \
potential but we shall keep it arbitrary for the time being so as to study \
the dependence of the observed indices, and especially the scalar spectral \
index ns on such exponent. The equations of motion are extracted by assuming \
the slow-roll condition is valid. Slow-roll indices along with observed \
indices are taken from arXiv:0412126.\
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Every parameter that ends with 1 is an auxiliary free parameter that needs to \
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potential are denoted while H is Hubble\[CloseCurlyQuote]s parameter and H2 \
the squared Hubble. Each parameter ending with dot implies time derivative \
for simplicity and Qt is an auxiliary function that depends on both the \
scalar field and the polarization of gravitational waves. Finally, indices \
\[CurlyEpsilon]1 through \[CurlyEpsilon]3 are the slow-roll indices of the \
model and ns, nt, r indicate the observed indices.\
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To study the inflationary era, one needs to insert as an input the value of \
the scalar field during the first horizon crossing to the observed indices. \
Such a value can be extracted by firstly finding the final value during the \
ending stage of the inflationary era by imposing that \[CurlyEpsilon]1 \
becomes of order O(1). Afterwards, by using the e-folding number \
N=\[Integral] Hdt, the initial value can be extracted as a function of N and \
\[CurlyPhi]f.\
\>", "Text",
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I use variable U to denote solutions hereafter while L is a random variable \
such that the initial value of the scalar field can be extracted.\
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3. Designation Of Free Parameters And Validity Of Approximations.\
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indices and derive results. Here, a blue shifted tensor spectral index (nt>0) \
can be achieved under the slow-roll assumption due to the presence of the \
Chern-Simons term in the initial gravitational action.\n\nThe model used in \
the article has a power-law Chern-Simons coupling v(\[CurlyPhi])=\
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The numerical values of the slow-roll indices during the first horizon \
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Such result is also expected to apply on the self check on the equations of \
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