Numerical calculation of secondorder perturbations

Ian HustonAstronomy Unit, Queen Mary, University of London

arXiv: 0907.2917with Karim Malik, accepted by JCAP

ϕ = ϕ0 + δϕ1 +1

2δϕ2

δϕ1′′ + 2Hδϕ1

′ + k2δϕ1 + a2M1δϕ1

= 0

δϕ2′′ + 2Hδϕ2

′ + k2δϕ2 + a2M2δϕ2

+S(δϕ1, δϕ1′) = 0

Malik, JCAP 0703 (2007) 004, astro-ph/0610864.

∫δϕ1(q

i)δϕ1(ki − qi)d3q

code():Following Salopek et al. (1989), Martin & Ringeval (2006)

61626364nend − n

−3

−2

−1

0

1

2

31 √2πk

3 2δϕ

1

×10−4

First order

010203040506070nend − n

10−14

10−13

10−12

10−11

10−10

10−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

|S|

Source term

5758596061nend − n

−4

−3

−2

−1

0

1

2

3

41 2πk

3 2δϕ

2

×10−93

Second order

v1.0:

1000+ k modes

Slow roll source term

Parallelisable

Need to go beyond 1st order

Convolution required

Next steps: full eqn, multi-field

arXiv: 0907.2917