Hello, please solve and post the answer in full detail and step-by-step. Thank you

$(4 points) Show that for a universe dominated by a slowly rolling scalar field with an expontential potential. \[ V(\phi) \pr$

(4 points) Show that for a universe dominated by a slowly rolling scalar field with an expontential potential. $V (?) ? exp [? \frac{2}{p} 8 ? G ?],$ the scale-factor grows like $a (t) ? t^{p}$ and $1 ? n_{n} = 2/ p$ . Current limits on $n_{n}$ rule out $p ? 60$ .

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Hello, please solve and post the answer in full detail and step-by-step. Thank you

$(4 points) Show that for a universe dominated by a slowly rolling scalar field with an expontential potential. \[ V(\phi) \pr$

(4 points) Show that for a universe dominated by a slowly rolling scalar field with an expontential potential.

V (?) ? exp [? \frac{2}{p} 8 ? G ?],

the scale-factor grows like

a (t) ? t^{p}

and

1 ? n_{n} = 2/ p

. Current limits on

n_{n}

rule out

p ? 60

.

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