As @DeepThought I also think that your best bet is to go with gravity=center as it is the only way I know to preserve aspect ratio.
however, if you wrap your drawable in a bitmap (as he suggests) it will not work on APIs different from 21,22 and 23. All the while on these same APIs images will always look stretched if you do not wrap them into a bitmap. which is why I would recommend you create 2 versions of your drawable layer-list and put one into drawable-v21 and the other in drawable-v24.
for v24 you can try:
<?xml version="1.0" encoding="utf-8"?><layer-list xmlns:android="http://schemas.android.com/apk/res/android">
<item
android:drawable="@android:color/white"
android:gravity="fill" />
<item
android:gravity="center"
android:src="@mipmap/logo" >
</item>
<item
android:gravity="center"
android:src="@drawable/splash" >
</item>
</layer-list>
for drawable-v21 you use
<?xml version="1.0" encoding="utf-8"?><layer-list xmlns:android="http://schemas.android.com/apk/res/android">
<item
android:drawable="@android:color/white"
android:gravity="fill" />
<item>
<bitmap
android:gravity="center"
android:src="@mipmap/logo" />
</item>
<item>
<bitmap
android:gravity="center"
android:src="@drawable/splash" />
</item>
</layer-list>
as for making the drawable fill the view horizontally without destroying aspect ratio I really dont know how to achieve this in xml. the only thing I can think of is oversizing your your splash_screen.xml file by setting the android:height and android:width parameters and facing the fact that on some slimmer devices a larger portion of the edges to the left and right of your SplashScreen will be cutt off.
....but if you are really obsessed about getting splash_screen.xml to fit all the width of the screen precisely there is always the total overkill solution. for that I recommend you read the following resource. it would imply you creating a bunch of alternative drawable resources depending on screen dp dimensions i.e. drawable-sw360dp, drawable-sw720dp and so on and then put in them different versions of your splash_screen.xml that have android:height and android:width taylored to each screen.