Gauss-Bonnet Braneworld Cosmology with Modified Induced Gravity on the Brane

<table>Variation of the deceleration parameter <svg height="12.1125" id="M151" style="vertical-align:-3.50804pt" version="1.1" viewbox="0 0 8.4750004 12.1125" width="8.4750004" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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q-30 16 -75 16q-58 0 -92 -27q-49 -39 -78.5 -112t-29.5 -136q0 -34 8.5 -52.5t21.5 -18.5q40 0 109.5 63.5t103.5 115.5q16 53 32 151z" id="x1D45E"></path></g>
</svg> versus <svg height="8.4250002" id="M152" style="vertical-align:-0.273pt" version="1.1" viewbox="0 0 8.5874996 8.4250002" width="8.5874996" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,8.013)"><path d="M475 445l-64 -69q-119 -128 -289 -280q27 6 81 -15q66 -26 102 -26q48 0 111 93l23 -19q-41 -84 -75.5 -116.5t-73.5 -32.5q-37 0 -147 53q-43 21 -63 7q-22 -15 -38 -41q-4 -7 -11 -7q-8 10 -8 26q0 38 47 83l292 273q-32 -5 -67 -1q-63 7 -105 7q-32 0 -53.5 -22
t-47.5 -67l-25 13q15 39 38 78q40 66 83 66q57 0 120 -12q52 -10 80 -10q29 0 67 42z" id="x1D467"></path></g>
</svg> for <svg height="11.125" id="M153" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 56.4375 11.125" width="56.4375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><path d="M495 86q-46 -47 -87 -72.5t-63 -25.5q-43 0 -16 107l49 210q7 34 8 50.5t-3 21t-13 4.5q-35 0 -109.5 -72.5t-115.5 -140.5q-21 -75 -38 -159q-50 -10 -76 -21l-6 8l84 340q8 35 -4 35q-17 0 -67 -46l-15 26q44 44 85.5 70.5t64.5 26.5q35 0 10 -103l-24 -98h2
q42 56 97 103.5t96 71.5q46 26 74 26q9 0 16 -2.5t14 -11.5t9.5 -24.5t-1 -44t-13.5 -68.5q-30 -117 -47 -200q-4 -19 -3.5 -25t6.5 -6q21 0 70 48z" id="x1D45B"></path></g><g transform="matrix(.017,-0,0,-.017,13.305,10.862)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,28.008,10.862)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,36.168,10.862)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.017,-0,0,-.017,40.044,10.862)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g><g transform="matrix(.017,-0,0,-.017,48.203,10.862)"><path d="M153 550l-26 -186q79 31 111 31q90 0 141.5 -51t51.5 -119q0 -93 -89 -166q-85 -69 -173 -71q-32 0 -61.5 11.5t-41.5 23.5q-18 17 -17 34q2 16 22 33q14 9 26 -1q61 -50 124 -50q60 0 93 43.5t33 104.5q0 69 -41.5 110t-121.5 41q-53 0 -102 -20l38 305h286l6 -8
l-26 -65h-233z" id="x35"></path></g>
</svg>. The transition from deceleration to the acceleration phase occurs at <svg height="11.2625" id="M154" style="vertical-align:-0.273pt" version="1.1" viewbox="0 0 36.174999 11.2625" width="36.174999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><path d="M475 445l-64 -69q-119 -128 -289 -280q27 6 81 -15q66 -26 102 -26q48 0 111 93l23 -19q-41 -84 -75.5 -116.5t-73.5 -32.5q-37 0 -147 53q-43 21 -63 7q-22 -15 -38 -41q-4 -7 -11 -7q-8 10 -8 26q0 38 47 83l292 273q-32 -5 -67 -1q-63 7 -105 7q-32 0 -53.5 -22
t-47.5 -67l-25 13q15 39 38 78q40 66 83 66q57 0 120 -12q52 -10 80 -10q29 0 67 42z" id="x1D467"></path></g><g transform="matrix(.017,-0,0,-.017,13.237,10.862)"><path d="M537 353q-54 -70 -120 -70q-47 0 -137 43q-78 38 -108 38q-55 0 -91 -57l-31 33q51 74 122 74q45 0 137 -44q76 -37 108 -37q55 0 91 57zM537 168q-54 -70 -120 -70q-47 0 -137 43q-78 38 -108 38q-55 0 -91 -57l-31 33q51 74 122 74q45 0 137 -44q76 -37 108 -37
q55 0 91 57z" id="x2248"></path></g><g transform="matrix(.017,-0,0,-.017,27.94,10.862)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg>.</table>

Advances in High Energy Physics

fig4

Figure 4

Figure 4: Gauss-Bonnet Braneworld Cosmology with Modified Induced Gravity on the Brane 