There are no direct references in Hindu scriptures as per which animals can be kept at a Hindu home. Today there are many animals that are kept based on Vastu. But the scriptures do give hints while narrating incidents and stories. Based on these hints, these animals can be kept (and cannot be kept) in the home as per Hindu religion. Some of these are lucky animals as they change luck.
As per Hindu religion, snakes are holy but they should not be kept as pets or in the compound of your house.
Similarly, it is not auspicious to keep bats, python, and scorpion as pets.
It is considered auspicious to keep deer as pets. It brings peace and prosperity. As per government rules, you are not supposed to keep wild animals like deer as pets.
Having rabbits at home brings prosperity. Keeping them is good for those looking to have children. It is also beneficial to children at home.
Keeping horse at home is considered beneficial in matters related to wealth.
Keeping birds especially parrot is considered beneficial. As per government rules, you are not supposed to keep parrots as pets.
Regarding cat, there are two schools of thoughts. Some people believe it beneficial. Some people are of the view that cats coming in and going out of house bring negative energy.
Keeping fish is considered highly meritorious.
If you have a cow at home then Goddess Lakshmi will constantly reside in the home. Ashwini Kumars and Lord Dhanvantari also reside in such homes. Thus there will be wealth and good health in such homes.
Having goats are considered helpful and they usher in prosperity.
Keeping dogs is considered good.
Having mongoose in the compound of your house is a sign of prosperity. It also ushers in peace.
Feeding birds daily at home wash away sins of previous birth.
Allowing birds to build a nest in your home is considered highly meritorious.
Feeding elephant with jaggery, coconut leaves and fronds, and sugarcane helps in alleviating all forms of unhappiness in life.
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As per Hindu religion, snakes are holy but they should not be kept as pets or in the compound of your house.
Similarly, it is not auspicious to keep bats, python, and scorpion as pets.
It is considered auspicious to keep deer as pets. It brings peace and prosperity. As per government rules, you are not supposed to keep wild animals like deer as pets.
Having rabbits at home brings prosperity. Keeping them is good for those looking to have children. It is also beneficial to children at home.
Keeping horse at home is considered beneficial in matters related to wealth.
Keeping birds especially parrot is considered beneficial. As per government rules, you are not supposed to keep parrots as pets.
Regarding cat, there are two schools of thoughts. Some people believe it beneficial. Some people are of the view that cats coming in and going out of house bring negative energy.
Keeping fish is considered highly meritorious.
If you have a cow at home then Goddess Lakshmi will constantly reside in the home. Ashwini Kumars and Lord Dhanvantari also reside in such homes. Thus there will be wealth and good health in such homes.
Having goats are considered helpful and they usher in prosperity.
Keeping dogs is considered good.
Having mongoose in the compound of your house is a sign of prosperity. It also ushers in peace.
Feeding birds daily at home wash away sins of previous birth.
Allowing birds to build a nest in your home is considered highly meritorious.
Feeding elephant with jaggery, coconut leaves and fronds, and sugarcane helps in alleviating all forms of unhappiness in life.
You might the following articles interesting
Dog in Hindu religion and scriptures
Mongoose in Hindu religion
Goat in Hindu scriptures